The elephant population of a nature preserve since 1990 is modeled by the exponential function f(x)=315⋅1.075x . Find the elephant population in 1990 and the percentage at which the population increases each year.

Answer 1

To find the elephant population in 1990 using the given model \( f(x) = 315 \cdot 1.075^x \), we need to evaluate the function at \( x = 0 \), since \( x \) represents the number of years since 1990.

1. Finding the population in 1990:

   \[ f(0) = 315 \cdot 1.075^0 = 315 \cdot 1 = 315 \]

   Therefore, the elephant population in 1990 was 315.

2. Finding the percentage increase in population each year:

The term \( 1.075 \) in the exponential function represents the growth factor. To find the percentage increase, we can calculate:

\[ \text{Percentage Increase} = (1.075 - 1) \times 100% = 0.075 \times 100% = 7.5% \]

Thus, the percentage increase in the elephant population each year is 7.5%.

In summary:

• The elephant population in 1990 was 315.
• The population increases by 7.5% each year.