Final answer:
The correct answer is option D. find how long it takes for the population to grow to 1134, we can use the formula for exponential growth. It takes approximately 7.6 years for the population to reach 1134.
Step-by-step explanation:
To find how long it takes for the population to grow to 1134, we need to use the concept of exponential growth. The formula for exponential growth is given by the equation: P(t) = P0 * (1 + r)^t, where P(t) is the population at time t, P0 is the initial population, r is the rate of growth as a decimal, and t is the time. In this case, the initial population is 215 and the rate of growth is 16.63% or 0.1663.
We can set up the equation as follows:
1134 = 215 * (1 + 0.1663)^t
Dividing both sides of the equation by 215:
(1 + 0.1663)^t = 1134/215
Taking the logarithm (base 10) of both sides:
t * log(1 + 0.1663) = log(1134/215)
Dividing both sides of the equation by log(1 + 0.1663):
t = log(1134/215) / log(1 + 0.1663)
Calculating the right side of the equation:
t ≈ 7.6 years
Therefore, it takes about 7.6 years for the population to grow to 1134.