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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.

- The elephant population in 1990 is 315, and the population increases by 1.075% each year.
- The elephant population in 1990 is 315, and the population increases by 7.5% each year.
- The elephant population in 1990 is 315, and the population increases by 0.75% each year.
- The elephant population in 1990 is 339, and the population increases by 7.5% each year.



Answer :

Answer:

B) The elephant population in 1990 is 315, and the population increases by 7.5% each year.

Step-by-step explanation:

We can find the percentage increase by subtracting 1 from the coefficient with the exponent containing x (not sure the coefficient is the right term).

We subtract 1 because it leaves the increased amount only, as 1 equals 100%. We get the number 1.075 - 1 = 0.075, which also equals 7.5%, giving us the answer B, or

*- The elephant population in 1990 is 315, and the population increases by 7.5% each year.*

Assuming x = the number of years, and 1990 was the year that this started, we can assume that x = 0, meaning we get the equation

315 * 1, which equals to 315. The elephant population is only 315, ruling out the answer choice D.

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