Please help with my word problems?

Solve the problem.

The rabbit population in a forest area grows at the rate of 6% monthly. If there are 260 rabbits in April, find how many rabbits (rounded to the nearest whole number) should be expected by next April. Use y=260(2.7)^0.06t? (I don't understand how to solve this problem?)

The size of the beaver population at a national park increases at the rate of 5.1% per year. If the size of the current population is 151, find how many beavers there should be in 4 years. Use the function f(x)=151e^0.051t and round to the nearest whole number. (This is what I got so far: f(4)=151e^0.051t)

Find the accumulated value of an investment of $20,000 at 12% compounded annually for 5 years. (I know annually is once year, so this is over a period of 5 years, so it would be five years and I would have to use the formual a=p(1 +r/n)^nt)

Find the accumulated value of an investment of $700 at 16% compounded quarterly for 2 years
(I know quarterly means 4 times, so if its for 2 years, it would 8 times, and I think the equation I would use would be a=p(1 +r/n)^nt)

the problem that is posted above is incorrect. The rabbit population in a forest grows at the rate of 6% monthly. If there are 160 rabbits in April, find how many rabbits should be expected by next April. Use y=160(2.7)^0.06t; t=rate of rabbit population growth;

Step 1: 0.06*(12)= .72
step 2: y=160(2.7)^.72
Step 3: y = 160(2.044475)
Step 4: y = 327.1160=327

for the rabbit question, t=12 (one year), so y=260(2.7)^((0.06)(12))

=534.15

I will do the last one for you

r/n = .16/4 = .04
nt = 2*4 = 8

Amount = 700(1.04)^8
=$958.00

The rabbit population in a forest area grows at the rate of 7% monthly. If there are 220 rabbits in April, find how many rabbits(rounded to the nearest whole number ) should be expected by the next April. Use y= 220(2.7)^0.07t

To solve the word problems, let's break them down step by step:

1. Rabbit population growth:
The formula given is y = 260(2.7)^(0.06t). Here's how you can solve the problem:

First, let's understand the formula:
- The initial population of rabbits is given as 260.
- The term (2.7)^(0.06t) represents the growth factor, where t is the number of months.
- 2.7 is the base for exponential growth, which represents 100% + 6% growth rate per month.
- 0.06 is the growth rate per month, expressed as a decimal.

To find the number of rabbits expected by next April, substitute t with the number of months from April to next April, which is 12.
- So, plug in t=12 into the formula: y = 260(2.7)^(0.06 * 12).
- Calculate the exponent first: 0.06 * 12 = 0.72.
- Substitute it back into the formula: y = 260(2.7)^(0.72).
- Evaluate 2.7^0.72 using a calculator, which gives approximately 4.015.
- Multiply 260 by 4.015 to get y ≈ 260 x 4.015 ≈ 1,044.
- Therefore, the expected number of rabbits by next April is approximately 1,044.

2. Beaver population growth:
The formula given is f(x) = 151e^(0.051t). Here's how you can solve the problem:

Similar to the previous problem, let's understand the formula:
- The initial population of beavers is given as 151.
- The term e^(0.051t) represents the growth factor, where t is the number of years.
- e is the base for exponential growth, which represents 100% + 5.1% growth rate per year.
- 0.051 is the growth rate per year, expressed as a decimal.

To find the number of beavers after 4 years, substitute t with 4 in the formula: f(4) = 151e^(0.051 * 4).
- Calculate the exponent first: 0.051 * 4 = 0.204.
- Substitute it back into the formula: f(4) = 151e^(0.204).
- Evaluate e^0.204 using a calculator, which gives approximately 1.226.
- Multiply 151 by 1.226 to get f(4) ≈ 151 x 1.226 ≈ 185.
- Therefore, there should be approximately 185 beavers after 4 years.

3. Accumulated value of an investment:
As you correctly mentioned, for compound interest, we can use the formula A = P(1 + r/n)^(n*t), where:
- A is the accumulated value
- P is the principal amount (initial investment)
- r is the interest rate (expressed as a decimal)
- n is the number of times interest is compounded per year
- t is the number of years

For the first problem, let's substitute the given values into the formula:
- P = $20,000
- r = 0.12 (12% expressed as decimal)
- n = 1 (since it's compounded annually)
- t = 5 years

Substitute these values into the formula: A = 20000(1 + 0.12/1)^(1*5).
- Simplify the exponent: (1 + 0.12)^5.
- Calculate the base: 1 + 0.12 = 1.12.
- Evaluate (1.12)^5 using a calculator, which gives approximately 1.762341683.
- Multiply 20000 by 1.762341683 to get A ≈ $35,246.83.
- Therefore, the accumulated value of the investment after 5 years is approximately $35,246.83.

For the second problem, let's substitute the given values into the formula:
- P = $700
- r = 0.16 (16% expressed as decimal)
- n = 4 (since it's compounded quarterly, 4 times per year)
- t = 2 years

Substitute these values into the formula: A = 700(1 + 0.16/4)^(4*2).
- Simplify the exponent: (1 + 0.16/4)^8.
- Calculate the base: 1 + 0.16/4 = 1.04.
- Evaluate (1.04)^8 using a calculator, which gives approximately 1.372956658.
- Multiply 700 by 1.372956658 to get A ≈ $961.07.
- Therefore, the accumulated value of the investment after 2 years is approximately $961.07.

I hope this helps you solve the word problems, understand the formulas, and apply them correctly.