Question

Which exponential function goes through the points (1, 8) and (4, 64)?

f(x) = 4(2)x

f(x) = 2(4)x

f(x) = 4(2)-x

f(x) = 2(4)-x

Answer 1

\(\normalsize\color{blue}{ f(x) = 4(2)^x \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{green}{ f(x) = 2(4)^x \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{red}{ f(x) = 2(4)^{-x} \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{darkgoldenrod}{ f(x) = 2(4)^{-x} \LARGE\color{white}{ \rm │ }}\)

Answer 2

plug in your points

Answer 3

ok give me a sec

Answer 4

I don't understand how to...

Answer 5

I am going to give you an example on the blue function.

\(\normalsize\color{blue}{ f(x) = 4(2)^x \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ (8) = 4(2)^{(1)} \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ (8) = 4(2) \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ (8) = 8 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ 8=8= \LARGE\color{white}{ \rm │ }}\) So it DOES go through (1,8)
──────────────────────────
\(\normalsize\color{blue}{ (64) = 4(2)^{4} \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ (64) = 4(16) \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ (64) = 64 \LARGE\color{white}{ \rm │ }}\)
\(\normalsize\color{blue}{ 64=64 \LARGE\color{white}{ \rm │ }}\)

So it goes through (4,64) as well.

Answer 6

The blue one is apparently it

Answer 7

so the blue is the only one that works