Question

Someone please help teach me this. MEDAL AND FAN!!!!

The expression below shows the population of squirrels in a forest after 3x years:

f(x) = 30(1.03)3x

Which of the following is an equivalent function?

f(x) = 30(3.0900)x

f(x) = 30(1.0927)x

f(x) = 10(1.0927)x

f(x) = 10(3.0900)x

Answer 1

\(\bf f(x) = 30(1.03)3x\quad or\quad f(x) = 30(1.03)3^x\quad or\quad f(x) = 30(1.03)^{3x}?\)

Answer 2

@jdoe0001 The last one

Answer 3

\(\bf (a^n)^{m}\iff a^{n\cdot m}
\\ \quad \\ \quad \\

f(x) = 30(1.03)^{{\color{blue}{ 3}}x}\implies f(x) = 30(1.03^{\color{blue}{ 3}})^{x}\implies ?\)

Answer 4

@jdoe0001 Man, I have no idea how to do this. Are their certain steps I am supposed to follow? If so can i get an example

Answer 5

well.... what would that exponentialized value give inside the parentheses?

Answer 6

1.092727? @jdoe0001

Answer 7

yeap.... thus \(\bf f(x) = 30(1.03)^{{\color{blue}{ 3}}x}\implies f(x) = 30(1.03^{\color{blue}{ 3}})^{x}\implies f(x)=30(1.092727)^x\)

Answer 8

and you can round that up to only say 1.0927

Answer 9

So we have f(x) = 30(1)^x right?

Answer 10

@jdoe0001