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?

There are 12 months a year, and if the growth is to be calculated four times a year, the interval would be every three months.

We use the variable
z as the number of 3 months per year

So,
x = z/4

Substituting, the new growth rate would be:
f(z) = 4(3)^(z/4)

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wifilethbridge wifilethbridge · Answer 2 · 2019-05-30T12:33:54+02:00

Answer:

[tex]f(x) = 4(1.32)^x[/tex] function is correct for Erin's purpose and the new growth rate is 32%

Step-by-step explanation:

Growth rate function: [tex]a(1+r)^x[/tex]--A

where r is the rate of growth

We are given that The function[tex]f(x) = 4(3)^x[/tex] represents the growth of a dragonfly population every year in a remote swamp.

Now Erin wants to manipulate the formula to an equivalent form that calculates four times a year, not just once a year

So, equation becomes: [tex]f(x) = 4(3^\frac{1}{4})^x[/tex]

[tex]f(x) = 4(1.32)^x[/tex]

Now on comparing with A

1.32=1+r

0.32=r

So, New growth rate = 0.32=32%

Hence [tex]f(x) = 4(1.32)^x[/tex] function is correct for Erin's purpose and the new growth rate is 32%