An exponential function for the amount in the account after T years if the interest of 8% is compounding annually on initial amount 1700 is: P_T = 1700(1.08)^T
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
How does compound interest works?Instead of calculating the interest on the initial amount, the compound interest repeats calculating interest on (old amount + interest to be paid).
For this case, we're specified that:
Initial amount deposited = $1700Rate of interest = 8% annual = 0.08 (converted percent to fraction).Let P be the inital amount, and r be the rate of interest compounding per unit of time (in decimal)
Let [tex]P_t[/tex] be the amount after t unit of time(same unit as the interest).
Then after 1 year, the new amount would be:
[tex]P_{t+1} = P_t + 100r \%\text{ of }P_t}\\P_{t+1}= P_t + P_t \times r\\P_{t+1} = P_t(1+r)[/tex]
Thus, we get:
[tex]P_t = P_{t-1}(1+r) = P_{t-2}(1+r)(1+r) = P_{t-2}(1+r)^2\\\\P_t = P_{t-t} (1+r)^t = P_0(1+r)^t[/tex]
where P₀ is the initial amount (as amount at t = 0 is initial amount)
Thus, we get:
[tex]P_t = P(1+r)^t[/tex]
Here, putting P = 1700, r = 0.08, and t = T, we get:
[tex]P_T = 1700(1.08)^T[/tex]
Thus, an exponential function for the amount in the account after T years if the interest of 8% is compounding annually on initial amount 1700 is: [tex]P_T = 1700(1.08)^T[/tex]
Learn more about compound interest here:
https://brainly.com/question/11897800
A bottle holds exactly 2/3 pint of liquid. How many 2/3-pint bottles can be filled from a 24-pint container
Answer:
36 number of 2/3-pint bottles can be filled from a 24-pint container
Step-by-step explanation:
Volume of the container is 24 pint
Volume of the bottle is 2/3 pint
Number of 2/3 pint bottles that can be filled from 24 pint container is
[tex]\frac{24}{\frac{2}{3} } \\= 24 * \frac{3}{2} \\= 12 * 3\\= 36[/tex]
36 number of 2/3-pint bottles can be filled from a 24-pint container
Amy had $28 dollar’s to spend on school supplies. After buying 7 pens, she had $20.30 left. How much did each pen cost including tax?
Answer:
Step-by-step explanation:
If Amy started with 28 dollars and bought 7 pens, then had 20.30 dollars, we can subtract to find the price of all 7 pens.
28-20.30=7.70 dollars
now to find the amount for EACH pen, we divide by 7
7.70/7=1.1
each pen costed Amy 1 dollar and 10 cents with tax
Answer:
$1.10
Step-by-step explanation:
$28-$20.30=$7.70
7.70 divided by 7= 1.10
so each pen must cost $1.10
h e l p
Zayn plans to deposit $850 into a savings account that pays 2.4% interest compounded annually. Angelo plans to deposit $860 into an account that pays 2.4% simple interest. They both plan to leave the money invested for 4 years. How much more money will Zayn have than Angelo at the end of the 4 years?
Answer:
Zayn= $928.72
Angelo= $880.64
Zayn has 48.08 more than Angelo.
Step-by-step explanation:
Answer:
zayn- 934.58
angelo- 880.64
Step-by-step explanation:
what is the circumference of the circle if r= 3.5 feet? Use 22/7 for pi
Answer:
circumference of circle=2πr
2×22/7×3.522hope it helps.
GEOMETRY 10TH GRADE HELP ASAP!!!
Answer:
Step-by-step explanation:
Please answer correctly! I will mark you as Brainliest!
Answer:
Volume=8
Step-by-step explanation:
[tex]volume[/tex]⇒[tex]\frac{1}{3}[/tex]×[tex](\frac{1}{2}[/tex]×[tex]3[/tex]×[tex]4^{2}[/tex]×[tex]4)[/tex]
⇒[tex]\frac{1}{3}[/tex]×[tex]3[/tex]×[tex]8[/tex]
[tex]Answer:8[/tex]
hope it helps...
have a great day!!!
Trent attaches his A+ test to the refrigerator with a circular magnet. Out of curiosity, he measures the magnet and calculates that it has a diameter of 4 centimeters. What is the magnet's area?
Answer:
12.6 cm²
Step-by-step explanation:
From the above question, the magnet is circular in shape
The area of a circle is given as:
= πr²
The area of the magnet = π × r²
Diameter = 4cm
r = Diameter/2 = 4cm/2 = 2cm
= π × (2cm)²
= 12.566370614cm²
Approximately = 12.6 cm²
The area of the magnet = 12.6cm²
El área de un terreno rectangular es de 144 metros cuadrados. Si la base es mayor 7 metros que la altura. ¿Cuáles serían las dimensiones reales? ¿Y su perímetro?
Altura = 16
Base = 9
(16 * 9 = 144)
Perímetro = 50
(16*2 + 9*2 = 50)
Liam plays guitar in a band called Cool. The
band is paid $421.74 for every performance. If
Cool averages 3.5 shows per month, how much
money will the band earn in 3 months?
Answer: $4,428.27
Step-by-step explanation:
First you have to find out how many shows are in three months. If there is 3.5 shows in one month, multiply this by three to get the amount in 3 months.
3.5 x 3 = 10.5 shows
Now multiply the amount the band makes in one show by the number of shows.
$421.74 x 10.5 shows = $4,428.27 over the course of three months.
Hope this helps!
Please help, any unnecessary answers will be reported. Thanks :)
Answer:
The area of the trapezoid is 152 square centimeters.
Step-by-step explanation:
The formula for finding the area of a trapezoid is [tex]\frac{a+b}{2} *h[/tex], where a and b are bases and h signifies the height.
Find the second base's length by adding 18 + 2 = 20.
Input values next:
[tex]\frac{18+20}{2} *8=152 cm^2[/tex]
Hope this helps; have a great day!
Jaylen and six of her younger siblings have ages that are consecutive. When they moved from San Francisco to Chicago, their ages (all seven of them) added up to 91. How old was Jaylen when they moved? Explain your thinking.
Answer:
Jaylen was 16 years old. She's the oldest.
Step-by-step explanation:
16 Jaylen
15 sibling 1
14 sibling 2
13 sibling 3
12 sibling 4
11 sibling 5
10 sibling 6
____________
91 Total
My thinking was that I started out dividing 91 by 7. That came out 13. So I knew the oldest one had to be older than 13.
ASAP, REALLY EASY If x = -3 then what is -x
Answer:
3
because it says -3
so yeah
atleast i hope Im so bad at math
Find the solution of the system of equations.
15x – 4y = -50
3x – 2y = –16
Answer:
x=-2, y=5. (-2, 5).
Step-by-step explanation:
15x-4y=-50
3x-2y=-16
---------------
15x-4y=-50
-5(3x-2y)=-5(-16)
------------------------
15x-4y=-50
-15x+10y=80
-------------------
6y=30
y=30/6
y=5
3x-2(5)=-16
3x-10=-16
3x=-16+10
3x=-6
x=-6/3
x=-2
PLEASE HELP!! Find the missing side of this right triangle
X
8
16
x=[?]
Answer:
The square root of 192
Step-by-step explanation:
It's just the Pythagoras theorem p much
Jasper's Pizzeria made 10 pizzas. 2 of the pizzas had pepperoni. What is the ratio of the number of pizzas without pepperoni to the number of pizzas with pepperoni?
Harrison ,Tad and dale ride their bikes to school Harrison rides 3/4 mile,Tad rides 3/8 and dale rides 3/6 mile. Compare and order and distances the boys ride from least the greatest
Answer:
3/8 , 3/6. 3/4
Tad drove the least miles because the miles ridden is less than both 3/6 and 3/4 miles
Dale rode the second greatest mile because the miles ridden is greater than 3/8 but less than 3/4
Harrison rode the greatest mile because the miles ridden is greater than both 3/6 and 3/8
Step-by-step explanation:
to order the miles ridden , convert the fraction to decimals. to do this, divide the numerator by the denominator
3/4 = 0.75
3/6 = 0.5 miles
3/8 = 0.374
if the opposite angle of rhombus are (2x)°and (3x-40°) then what is the value of x?
Options :
A. 100°
B.80°
C.160°
D.40°
6(x+4)+1= What is the answer to this great math problem
Answer:
x = -25/6
Step-by-step explanation:
6 (x + 4) + 1 = 0
6x + 24 + 1 = 0
6x + 25 = 0
6x = -25
x = -25/6
Dante invests $3,500 and learns 2% in simple interest each year assuming he makes no additional deposits or withdrawals how much will his investment be worth in 5 years
Answer:
answer in the picture
Step-by-step explanation:
HELLLLLLPPPPPPPPPPPPP
Which justification can be used to demonstrate the graph is correct?
The justification (D) shading is to the left because (0, 0) does not satisfy the inequality option (D) is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.
We have inequality:
[tex]\rm x+3.5 < \dfrac{1}{10}(y-2)^2[/tex]
If plug (0, 0)
0 + 3.5 < 4/10
Which is not true.
Thus, the justification (D) shading is to the left because (0, 0) does not satisfy the inequality option (D) is correct.
Learn more about the inequality here:
brainly.com/question/19491153
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Which equation in standard form has a graph that passes through the point (-3, 2) and has a slope of 4/3 ?
Answer:
y = 4/3x + 6
Step-by-step explanation:
y = 4/3x + b
2 = 4/3(-3) + b
2 = -4 + b
6 = b
y = 4/3x + 6
Help ASAP I really need an answer I don't need links please and if you don't know that answer just don't answer
Answer:
113
Step-by-step explanation:
note: to find the circumference of a circle using the radius, you use this equation -- 2[tex]\pi[/tex]r. since the radius is 18, you make the equation 2[tex]\pi[/tex]18. that gets you 36[tex]\pi[/tex], which, if put into the calculator, is about 113.
Which fraction is a name for the point that is labeled with the question mark on the number line?
A) 4/8
B) 3/4
C) 1/4
D) 2/4
Answer:
The awnser is C it is 2/8 simplified to 1/4
Step-by-step explanation:
Find the measure of angle 1
Answer:28
Step-by-step explanation:
solve the quadratic equation
8x^2+16x+8=0
Answer:
8x²+16x+8=0
x²+2x+1=0
D=4-4=0
x0=-2/2=-1
Answer:
x = -1Step-by-step explanation:
[tex]8x^2+16x+8=0[/tex] {divide both sides by 8}
[tex]x^2+2x+1=0\\\\a=1\,,\quad b=2\,,\quad c=1\\\\x=\dfrac{-2\pm\sqrt{2^2-4\cdot1\cdot1}}{2\cdot1}=\dfrac{-2\pm\sqrt{4-4}}2=\dfrac{-2\pm0}2=-1[/tex]
please please help i have three questions left for this lesson
9514 1404 393
Answer:
y = -|x -1| +2
Step-by-step explanation:
The transformation ...
-f(x -h) +k
reflects function f(x) over the x-axis, translates it 'h' units to the right and 'k' units up.
Your absolute value function is reflected over the x-axis, then translated 1 unit right (h=1) and 2 units up (k=2). Putting these values in the function, we have ...
y = -abs(x -1) +2
y = -|x -1| +2
What angles are congruent to angle 1
Answer:
<6 and <3 are congruent to <1.
Answer:
angle 7
Step-by-step explanation:
angle 1 + angle 5 =180
and angle 5 = angle 7
angle 1 is congruent to angle 7
it's incorrect
Please help
If you currently make 3200 per month and you are given a raise to 3400 per month, what is the percent change of your salary?
Answer:
6.25%
Step-by-step explanation:
% change= (chnage/original salary) × 100%
Change = new salary - original salary
Hence = 3400-3200=200
% change= (200/3200)×100%= 6.25%
If 2% of a number equals 9, find 4% of that number.
Answer:
18
Step-by-step explanation:
The number you are getting the percent from is 450