Question

test information
description
instructions
multiple attempts this test allows multiple attempts.
force completion this test can be saved and resumed later.
your answers are saved automatically.
question completion status:

moving to another question will save this response.
question 5
which of the following exponential functions passes through the points (6, 80) and (12, 160)?
$f(x) = 20(2)^{x/6}$
$f(x) = 20(2)^{x/4}$
$f(x) = 40(2)^{x/3}$
$f(x) = 40(2)^{x/6}$
$f(x) = 40(2)^{x/2}$
$f(x) = 20(2)^{x/3}$

Explanation:

Step1: Test the first point (6,80) in each function

For \( f(x) = 20(2)^{x/6} \): Substitute \( x = 6 \), we get \( f(6)=20(2)^{6/6}=20\times2 = 40
eq80 \). So this is wrong.
For \( f(x) = 20(2)^{x/4} \): Substitute \( x = 6 \), \( f(6)=20(2)^{6/4}=20\times2^{1.5}=20\times2\sqrt{2}\approx56.57
eq80 \). Wrong.
For \( f(x) = 40(2)^{x/3} \): Substitute \( x = 6 \), \( f(6)=40(2)^{6/3}=40\times4 = 160
eq80 \). Wrong.
For \( f(x) = 40(2)^{x/6} \): Substitute \( x = 6 \), \( f(6)=40(2)^{6/6}=40\times2 = 80 \). This works for the first point. Now check the second point (12,160).
Substitute \( x = 12 \) into \( f(x) = 40(2)^{x/6} \), we get \( f(12)=40(2)^{12/6}=40\times4 = 160 \). This works for the second point.
We can also check other functions for confirmation.
For \( f(x) = 40(2)^{x/2} \): Substitute \( x = 6 \), \( f(6)=40(2)^{3}=40\times8 = 320
eq80 \). Wrong.
For \( f(x) = 20(2)^{x/3} \): Substitute \( x = 6 \), \( f(6)=20(2)^{2}=20\times4 = 80 \). Now check \( x = 12 \), \( f(12)=20(2)^{4}=20\times16 = 320
eq160 \). Wrong.

Answer:

\( f(x) = 40(2)^{x/6} \)