Assume the population was 724 when t=0, and 4 years later it became 2334. 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 can use the concept of exponential growth. Exponential growth is modeled by the formula:
Population = Initial Population × (1 + Growth Rate)^t
Where:
- Initial Population is the population at the starting point (t=0)
- Growth Rate is the rate at which the population is growing
- t is the time in years
In this case, we are given that the population was 724 when t=0 and it became 2334 after 4 years. We can use this information to find the growth rate:
2334 = 724 × (1 + Growth Rate)^4
To isolate the growth rate, we can rearrange the equation:
(1 + Growth Rate)^4 = 2334/724
Now, we can solve for Growth Rate by taking the 4th root of both sides:
1 + Growth Rate = (2334/724)^(1/4)
Growth Rate = (2334/724)^(1/4) - 1
Once we have the growth rate, we can substitute it back into the exponential growth formula to find the population when t=12:
Population = 724 × (1 + Growth Rate)^12
Population=724^tk
at 4 years
2334=724^4k
log of both sides
log2334=4k*log724
k= log2334/(4*log724)
k=.294
Population=724^(.294t)