Question

A wolf population is growing exponentially. In 2011, 129 wolves were counted. By 2013, the population had reached 236 wolves. Write the equation representing the population N of wolves over time t. Write your answer in the form a(b)^t. Round your b value to 3 decimal places. ​

Answer 1

The exponential growth equation for the wolf population, where 2011 is the base year (t = 0), is N = 129(1.353)^t, with the initial population in 2011 being 129 and the growth factor 'b' being approximately 1.353 after rounding to three decimal places.

Step-by-step explanation:

To find the equation of the exponentially growing wolf population, we need to use the formula N = a(b)^t, where N is the population size at time t, a is the initial population size, and b is the growth factor per unit of time.

Since the population was 129 in 2011 and grew to 236 by 2013, we can set 2011 as the base year, which means t = 0 for 2011 and t = 2 for 2013.

The initial population size (a) in 2011 was 129. So we have two points: (0, 129) and (2, 236).

We can set up the equations as follows:

• 129 = a(b)^0
• 236 = a(b)^2

From the first equation, since any number raised to the power of 0 is 1, we have a = 129.

To find b, we use the second equation:

236 = 129(b)^2

Now solve for b:

b^2 = 236 / 129

b^2 ≈ 1.8295

b ≈ √1.8295

b ≈ 1.353 (rounded to 3 decimal places)

The exponential growth equation is:

N = 129(1.353)^t