Given:
f(x) is an exponential function.
[tex]f(-3.5)=25, f(6)=33[/tex]
To find:
The value of f(6.5).
Solution:
Let the exponential function is
[tex]f(x)=ab^x[/tex] ...(i)
Where, a is the initial value and b is the growth factor.
We have, [tex]f(-3.5)=25[/tex]. So, put x=-3.5 and f(x)=25 in (i).
[tex]25=ab^{-3.5}[/tex] ...(ii)
We have, [tex]f(6)=33[/tex]. So, put x=6 and f(x)=33 in (i).
[tex]33=ab^{6}[/tex] ...(iii)
On dividing (iii) by (ii), we get
[tex]\dfrac{33}{25}=\dfrac{ab^{6}}{ab^{-3.5}}[/tex]
[tex]1.32=b^{9.5}[/tex]
[tex](1.32)^{\frac{1}{9.5}}=b[/tex]
[tex]1.0296556=b[/tex]
[tex]b\approx 1.03[/tex]
Putting b=1.03 in (iii), we get
[tex]33=a(1.03)^{6}[/tex]
[tex]33=a(1.194)[/tex]
[tex]\dfrac{33}{1.194}=a[/tex]
[tex]a\approx 27.63[/tex]
Putting a=27.63 and b=1.03 in (i), we get
[tex]f(x)=27.63(1.03)^x[/tex]
Therefore, the required exponential function is [tex]f(x)=27.63(1.03)^x[/tex].
Solve for b. b + 2 = 4.6
b=6.6
b=4.12
b=2.6
b=2.3
Answer:
b=2.6
Step-by-step explanation:
b+2=4.6
Subtract both sides by 2 to isolate b
b+2-2=4.6-2
b=2.6
Therefore, b is equal to 2.6.
I hope this helps!
i need the area of a rectangle, the middle is 5ft the right is 6ft and the bottom is 5ft. thank u
Answer:
length times width for area so its 5x6=30
What is the area of the image below?
I will mark brainliest!!!
Answer:
116 square cm
Step-by-step explanation:
Find the area of each shape
7*10=70
4*4=16
1/2(15)*4=30
70+16+30=116
Pls help ASAP.......
Answer:$25.50
Step-by-step explanation:
Convert the problem to an equation using the percentage formula: P% * X = Y.
P is 10%, X is 150, so the equation is 10% * 150 = Y.
Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10. Im not sure if this is the nearest cent but here are the steps to find the nearest cent.
Answer:
it will cost $25.5
Step- by-step explanation:
so $30 by 15 divide it by 1 hundred so and will by equal to $4.5
An angle measures 56° more than the measure of its supplementary angle. What is the measure of each angle?
Answer:
62,118
Step-by-step explanation:
Let one angle = x
So, other angle = x +56
x +x +56 = 180 {Combine like terms}
2x + 5 6 = 180 {Subtract 56 form both sides}
2x = 180 - 56
2x = 124 {Divide both sides by 2}
x = 124/2
x = 62
Other angle = 62 + 56 = 118
Which equation has imaginary roots?
A. x(5 + x) = 8
B. x(5 - x) = -3
C. x(x + 6) = -10
D.(2x + 1)(x – 3) = 7
hey I'm chloe can you help me, i will give Brainlest, Thank you :)
Cylender A has a radius of 4 inches and height of 2 inches. Cylinder B has a radius of 2 inches. What is the height of cylinder B if both cylinders have the same volume?
Answer:
Cylinder B: The height would be 8 inches.
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
V = A * h
CA = 4² = 16 * 2 = 32π
CB = 2² = 4 * 8 = 32π
The radius of a circle is 17 m. Find its area in terms of pi.
Answer:
289m²
Step-by-step explanation:
Area of circle =πr²=π×17²=289m² when r=radius =17m
Triangle ABC is congruent to triangle DCE by...
SSS
AAS
ASA
SAS
Answer:
ASA
Step-by-step explanation:
please help me with this and explain. It’s due in a bit :/
Answer:
choice D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
they have similar angles and similar sides, and the description choice D gives is also correct
find the value of x3-1 if x= 0, 1,-1
Step-by-step explanation:
Given
x³ - 1
When x = 0
0³ - 1 = - 1When x = 1
1³ - 1 = 0when x = - 1
( -1)³ - 1 = - 2Hope it will help :)❤
A rectangle has a length of 7 cm and a width of (3x+4)cm. Which expression represents the perimeter?
Answer:
2{7 + (3x + 4)} represents the perimeter of the rectangle
Ruben adds some water to a glass of juice. The ratio of water to juice in his glass in now 4:6. Which fraction below represents this ratio? A 3/5 C 2/3 B 3/2 D 2/5
Answer:
C
Step-by-step explanation:
since we're being told to convert the ratio to fraction then it is C. note that 4 ratio is also the same as dividing 4 by 6
find the mean of the given data. 147 141 120 124 128
Write an equation in slope-intercept form of the line shown.
Answer:
y=2x-2
Step-by-step explanation:
The slope is 2 and your y intercept is already given as -2.
Slope intercept is basically y=mx+b
plug it in so you get y=2x-2
For each fraction, select the most appropriate estimate. 36 40 choose.. 1 3 choose.. 70 100 choose.. 1 8 choose.. Options: Closest to 0 Closest to one half Closest to 1
Answer:
Convert each fraction to its percentage form:
= 36 / 40
= 90%
= 1/3
= 33.3%
= 70/100
= 70%
= 1 / 8
= 12.5%
Looking at the percentages:
= 36 / 40 is closest to 1.
= 1/3 and 70/100 are closest to one half which is 50%
= 1/8 is closest to 0.
how do you prove something as a parallelogram?
A sports tournament has d teams. Each team has 15 players. Using d, write an expression for the total number of players in the tournament.
Answer:
d x 15=total players.
Step-by-step explanation:
dx15=total number of players in the tournament.
Answer:
15d
Step-by-step explanation:
If there are d teams and 15 people in each team d x 15 = 15d
Help pls!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
(4p^2+3)(p+2)
Step-by-step explanation:
what is x7 * x-5 ?????????
[tex]7x \times x - 5[/tex]
Pemdas!
7x·1x=7x
[tex]7x - 5[/tex]
This equation can't be evaluated, but you could make up. an answer by yourself, this is just the other way of saying x7·x-5
Answer:
7x²-5
Step-by-step explanation:
hope it helps
complete the square to solve 3x^2+12x=9
A. x=3+√6
B. x=2+√7
C. x=-2+√7
D. x=-2+√13
Step-by-step explanation:
3 {x}^{2} + 12x - 9 = 0
[tex] \frac{ - (12) \binom{ + }{ - } \sqrt{ {12}^{2} - 4(3)( - 9)} }{2(3)} [/tex]
The combined height of one fur tree and one pine tree is 21 meters. The higher of 4 fir trees stacked on top of each other is 24 meters taller that the one pine tree. How tall are the types of trees that Logan genetically engineered?
Answer: Fur tree = 6 meters, pine tree = 15 meters
Step-by-step explanation:
Lets say the height of one fur tree is x
the height of one pine tree is y
so x+y=21 and 4x=24
x = 6
y = 15
PLEASE HELP WILL GIVE BRAINLIEST!!!
Answer:
angle U ( the third option down)
Step-by-step explanation:
Which systems of equations have infinite solutions
2x+y 31
+ y = 18
2x+y 10
изу +7
y 14 - 2x
0x3y12
y 13 - 2
1x 3.10
2x + y 14
X 13 - 2y
2x+y 17
Ox3y - 61
Justin's pay is represented by this line graph.
Pay (dollars)
300
280
260
240
220
200
180
160
140
120
100
80
60
40+
20+
0
10 20 30 40
Time Worked (hours)
How much is Justin paid for one hour of work?
$6.50
$7.50
$8.00
I REALLY NEED HELP WITH THIS PROBLEM
Answer:
B
Step-by-step explanation:
it would be (4^2=16-1=15)/(-4+1=-3)
-15/3=-5
make p the subject of the formula A=p+prt÷100
Answer:
p = a - prt x 100
Step-by-step explanation:
a = p + prt ÷ 100
a - prt = p ÷ 100
a - prt x 100 = p
Hope this helps. :)
Explain how you would find 90% of 120 will give brainliest if correct
Find the missing side (to 2dp)
Answer:
x = 17.74 cm
Step-by-step explanation:
tan 29 = x/32
0.5543 = x/32
x = 17.74 cm
Answer:
17.74 to 2 dp.
Step-by-step explanation:
tan 29 = x/32
x = 32 tan 29
= 17.7379.
Please help me guys !
Answer:
A) 3 cents difference
Step-by-step explanation:
Fresh fruity mints costs 20 cents per piece:
$2.40 / 12 = 20 cents
Circle mints costs 17 cents per piece:
$5.00 / 30 = 16.6666 cents which rounds to 17
20 - 17 = 3
Answer is A