Assume that a population was 853 when t=0, and 3 years later it became 2314.
Assuming the population grows exponentially, write a formula for the size of the population in t years:
Population =
What is the population when t = 12?:
To write a formula for the size of the population in t years, we need to use the exponential growth formula. The exponential growth formula is given by:
P = P0 * (1 + r)^t
Where:
P is the population after t years,
P0 is the initial population at t=0,
r is the growth rate, and
t is the time in years.
We are given that the initial population at t=0 is 853. Therefore, P0 is 853.
To find the growth rate (r), we can use the following equation:
P = P0 * (1 + r)^t
Substituting the values we know, we get:
2314 = 853 * (1 + r)^3
Dividing both sides of the equation by 853, we get:
(1 + r)^3 = 2314/853
Take the cube root of both sides:
1 + r = (2314/853)^(1/3)
Subtract 1 from both sides:
r = (2314/853)^(1/3) - 1
Now that we have the growth rate (r), we can substitute it into the exponential growth formula to find the population when t = 12:
Population = 853 * (1 + r)^12
Calculating the population using the provided formula will give us the answer.
clearly,
p = 853*e^(kt)
so, since
p(3) = 2314, k = 1/3 log(2314/853) = .3326577