Question

The function f(x) = 2(3)x represents the growth of a dragonfly population every year in a remote swamp. Rose wants to manipulate the formula to an equivalent form that calculates seven times a year, not just once a year. Which function is correct for Rose's purpose, and what is the new growth rate?

Answer 1

below ----->

Explanation:

To calculate the growth of the dragonfly population seven times a year, instead of just once a year, we need to adjust the function f(x) = 2(3)^x.

To do this, we can divide the exponent by the number of times the population grows in a year, which is 7 in this case.

The new function that calculates the growth seven times a year would be f(x) = 2(3)^(x/7).

Let's break it down step by step:

1. We start with the original function: f(x) = 2(3)^x.

2. We divide the exponent x by 7 to represent the growth happening seven times a year: f(x) = 2(3)^(x/7).

Now, let's find the new growth rate.

The growth rate is determined by the base of the exponential function, which is 3 in this case.

In the original function, the growth rate was 3.

In the new function, the growth rate remains the same since we only adjusted the frequency of growth. Therefore, the new growth rate is still 3.

the correct function for Rose's purpose is f(x) = 2(3)^(x/7), and the new growth rate remains 3.