The function f(x) = 4(3)x represents the growth of a dragonfly population every year in a remote swamp. erin wants to manipulate the formula to an equivalent form that calculates four times a year, not just once a year. which function is correct for erin's purpose, and what is the new growth rate?

New growth rate = 32%

Step-by-step explanation:

∵ The exponential growth function is,

Where,

a = initial value,

b = growth rate per period,

x = number of period,

Here, the given function that shows the population growth every year,

By comparing,

Initial population, a = 4,

Let r be the rate per 4 times a year,

Thus, the function that shows the population growth four times a year,

According to the question,

Taking log  both sides,

By graphing calculator,

Hence, the required function would be,

And, rate per period is 32%.