Question

Type the correct answer in each box. Use numerals instead of words. Sabrina is researching the growth of a population of horses on a ranch. She models the population of horses using the function below, where n is the number of years after she begins the research, and b is an unknown base.w(n)=150×b^n

Based on the model, the initial number of horses is _____.

If b=1.35, the annual percent growth rate of the number of horses would be _____%.

a) 150; 35
b) 150; 135
c) 135; 150
d) 35; 150

Answer 1

The initial number of horses on the ranch is 150. If the base of the exponential growth function is 1.35, the annual percent growth rate of the horse population is 35%.

Step-by-step explanation:

Sabrina is using an exponential function to model the population growth of horses on a ranch. The function is w(n) = 150×b^n, where n represents the number of years after the research begins, and b is the growth factor or base of the exponential function. To find the initial number of horses, we evaluate the function at n = 0, which results in w(0) = 150×b^0 = 150×(1) = 150. Therefore, the initial number of horses is 150.

If we take b = 1.35, this represents a 35% increase each year, because the base of an exponential growth function is equal to 1 plus the decimal equivalent of the percentage growth rate. So if b = 1.35, the actual growth rate is 1.35 - 1 = 0.35, which is 35%. Thus, the annual percent growth rate of the population of horses is 35%.