Laura invested $1000 in a college saving account for her children that had an annual interest rate of 11% compounded continuously after 20 years how much money is in her account

The deer population in 5 years is approximately 294 deer.

A rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay. Over time, exponential functions monitor constant growth. Examples from the actual world include radioactive decay, compound interest, and bacterial proliferation.

a. To solve the differential equation dP/dt = −0.1P, we can separate the variables and integrate:

dP/P = −0.1 dt

Integrating both sides gives:

ln|P| = −0.1t + C

where C is the constant of integration. To solve for C, we can use the initial condition that P = 495 when t = 0:

ln|495| = −0.1(0) + C

C = ln|495|

Substituting this value of C back into the equation gives:

ln|P| = −0.1t + ln|495|

Simplifying using logarithm properties, we get:

ln|P/495| = −0.1t

Exponentiating both sides gives:

|P/495| = e^−0.1t

Taking the absolute value off and multiplying both sides by 495, we get:

P = 495e^−0.1t

To find the deer population in 5 years, we can substitute t = 5 into the equation:

[tex]P = 495e^{-0.1(5)} = 294[/tex] deer (rounded to the nearest deer).

Therefore, the deer population in 5 years is approximately 294 deer.

b. To find an equation for the deer population P(t) in terms of t and k for the period after 5 years, we can use the differential equation:

dP/dt = k(650−P)

Separating the variables and integrating, we get:

∫dP/(650−P) = ∫k dt

Using partial fraction decomposition and integrating, we get:

ln|650−P| = −kt + C

where C is the constant of integration. To solve for C, we can use the initial condition that P = 294 when t = 5:

ln|650−294| = −k(5) + C

C = ln|356| + 5k

Substituting this value of C back into the equation gives:

ln|650−P| = −kt + ln|356| + 5k

Simplifying using logarithm properties, we get:

ln|(650−P)/356| = −kt

Exponentiating both sides gives:

[tex]|(650-P)/356| = e^{-kt[/tex]

Taking the absolute value off and multiplying both sides by 356, we get:

[tex]650-P = 356e^{-kt[/tex]

Solving for P gives:

[tex]P = 650-356e^{-kt[/tex]

Therefore, the equation for the deer population P(t) in terms of t and k for the period after 5 years is P = 650−356e^−kt.

c. Using the growth model from part b), if the deer population is 350 one year later, we can substitute t = 1 and P = 350 into the equation and solve for k:

350 = 650−356e^−k

Solving for [tex]e^{-k[/tex] gives:

[tex]e^{-k = (650-350)/356 = 3/2[/tex]

Taking the natural logarithm of both sides gives:

−k = ln(3/2)

Solving for k gives:

k = −ln(3/2) ≈ 0.4055

Therefore, k ≈ 0.4055.

d. Using the growth model from part b) and the value of k from part c), the long-term behavior of the deer population as t → ∞ is determined by the limit:

lim P(t) as t → ∞

We can use the fact that [tex]e^{-kt[/tex]approaches 0 as t →

Learn more about exponential growth and decay here:

https://brainly.com/question/17161065

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Answer:

there's a total of 388.8 kids in the class but you can have 0.8 of a person and you can't round a person up so just 388

Step-by-step explanation:

tldr: 388 people

Step-by-step explanation:

This would be the point of intersection.

If you are not given the graph, make the equations equal since they are both y = ____.

x + 3 = x - 1

  -3         -3

x = x - 4

-x  -x

-2x = -4

/-2     /-2

x = 2

So the answer would be D) (2,1)

Answer:

the thrid answer

Step-by-step explanation:

Answer: 8.3 m

Step-by-step explanation:

Given

The angle of declination is [tex]50^{\circ}[/tex]

Earthworm is [tex]7\ m[/tex] away from the base of the tree

Suppose h is the height of the tree

from the figure, we can write

[tex]\Rightarrow \tan 50^{\circ}=\dfrac{h}{7}\\\\\Rightarrow h=7\tan 50^{\circ}=8.3\ m[/tex]

Answer:

there are 2oranges out if 6 fruit so this would mean your fraction of oranges is 2/6

Step-by-step explanation:

I hope this helps!

Answer:

x = 13

Step-by-step explanation:

3x + 5 = 44

3x = 39

x = 13

Answer:

x=  1 /3 y+ −5 /3

y=3x+5

Step-by-step explanation:

brainliest?

Answer:

Give my man brainliest

Step-by-step explanation:

Don't report this

Answer:

i got you!

Step-by-step explanation:

6(x + 2)

3(x + y)

5(2x + 5)

3(27x + 16)

8(3x +2y + 1)

3( 1 + 8x +2y)

9( 9x -4y- 2)

6 (9x +2 )

Answer:

6(x+2), 3(x+y), 5(2+5x), 3(27x+16), 8(3x+2y+1), 3(1+8x+2y), 9(9x−4y−2), 6(9x+2).

Answer: Oop if you put that on spotify i would listen to that on repeattttttt

Answer: 590

Step-by-step explanation: 17$ is 17% and times that by 3 because of the 3 weeks, then you have 68$ and I just added 300 to the rest and then just subtracted 68$

What can I say exept your not welcome :D

Answer:

Step-by-step explanation:

    - 50 + (5 / 13)p         this says negative 50 plus 5/13 times p

if p = -26                      what does this epression evaluate to?

- 50 + (5 / 13) × p      p = -26      substitute the value of p into the expression

- 50 + (5 / 13) × (-26)      

- 50 + (5 (-26) / 13)                 I just rewrote the expression to make it clearer

                                               that the -26 in -26/1 and the  5 in 5 / 13    are

                                              both in the numerator over denominator 13

 - 50 + (5 (-26) / 13)              -26 / 13  evaluates to -2

 -50  + (5)(-2)    

 -50  + (-10)

 -50 - 10

 -60                

Answer:

very cute

Step-by-step explanation:

Ian even know him until now but he mad fine

Answer:

Use photo math, it will explain it all in different forms

Answer:

$1100 approx

Step-by-step explanation:

Given data

SImple interest = $55

Time= 5 months in years = 5/12= 0.42 years

rate= 12%

Let the sum be P, that is the principal

The expression for the interest is given as

SI=PRT/100

substitute

55= P*12*0.42/100

Cross multiply

5500=5.04P

P= 5500/5.04

P= 1091.2

Hence the Principal is $1100 approx

Answer:

If you use the formula it should help for your answer.

Step-by-step explanation:

Answer:

The question is corrected to get;

405,852

Step-by-step explanation:

The expression of the description when written as follows;

'I am a 6-digit number one of my 4s is worth 400,000. The other 5 is worth 1/100 as much. My 5 is worth 5 (10s). y 8 is worth 800. My 2 is' worth 2. My other digit is a 0 what number am I, we have;

The number of digits in the number = 6

The position of the number 4 = 100,000s, we have;

4xx,xxx

The position of the number 5 is in the 10s position, we have;

4xx,x5x

The other 5 = 50100 = 0.5

Therefore, we have;

4xx,x5x.5

The position of the 8 is the 100s, to give;

4xx,85x.5

The number 2 is in the unit position, therefore, we have;

405,852

Answer:

7x^2 - x -3

Step-by-step explanation:

(6x^2+3x) + (x^2 - 4x -3)

We have to use distributive property first to get rid of the parenthesis, so you simply have to multiply the positive (+) symbol with everything inside the second set of parenthesis.

+ * x^2 = x^2

+ * -4x = -4x

+ * -3 = -3

Now, we rewrite the equation which is

6x^2 + 3x + x^2 - 4x -3

Now you simply combine like terms.

6x^2 + x^2 = 7x^2

3x-4x = -x

The answer will be

7x^2 - x -3

Hope this helps!!

-Ketifa

(Can I get brainliest?)

Answer: Answer is 1

Step-by-step explanation:

Answer: just do 10.8×9×6 and divide the answer by two

Step-by-step explanation:

Answer:

the area is 27

Step-by-step explanation:

[tex]9 \times 6 \div 2 = 27[/tex]

Answer: 12

Step-by-step explanation: you need to look at the paper

Answer: 336

Step-by-step explanation:

Multiply all three numbers

Answer:

a

Step-by-step explanation:

Answer:

dunno

Step-by-step explanation:

Answer:

y=−1/3 y+5/3

Step-by-step explanation:

PLS BRAINLIEST

ill tell you all the 4 math algebra calculators if you do

Answer:

the range of the data is 6 points

Step-by-step explanation:

Answer:

4 cups

Step-by-step explanation:

Number of cups of milk for 5 servings = [tex]2\frac{1}{2} =\frac{5}{2}[/tex] cups

First find number of cups of milk for 1 serving.

Number of cups of milk for 1 serving = [tex]\frac{\frac{5}{2} }{5}=\frac{1}{2}[/tex] cup

Now find umber of cups of milk for 8 servings.

Therefore,

Number of cups of milk for 8 servings = [tex]8(\frac{1}{2})=4[/tex] cups