Exponentials: Application 3

Exponentials

A certain population of eagles starts at 50, but is declining by 4% per year. Write an equation to model this population.

Step 1. Determine the initial value. The population starts at 50 eagles.

a = 50

Step 2. Write the rate as a decay factor. The population is declining by 4%. Subtract this from 100%. 100% - 4% = 96%; translate to a decimal.

b = 0.96

Step 3. Write the equation.

y = a ^.b^x

y = 50(0.96)^x