SOLUTION
We want to solve the question below
write an exponential equation in the form y = ab* whose graph passes through points (-3, 24) and (-2, 12).
Now an exponential equation is written in the form of
[tex]y=a(b)^x[/tex]
Now we will substitute -3 for x and 24 for y, we have
[tex]24=a(b)^{-3}[/tex]
Also substituting -2 for x and 12 for y, we have
[tex]12=a(b)^{-2}[/tex]
Dividing equation 2 by equation 1, we have
[tex]\begin{gathered} \frac{12}{24}=\frac{a(b)^{-2}}{a(b)^{-3}} \\ \frac{1}{2}=b^{-2-(-3)} \\ \frac{1}{2}=b^{-2+3} \\ \frac{1}{2}=b \\ b=\frac{1}{2} \end{gathered}[/tex]
Now substitute this value of b into equation 2, we have
[tex]\begin{gathered} 12=a(b)^{-2} \\ 12=a(\frac{1}{2})^{-2} \\ 12=a\times(2^{-1})^{-2} \\ 12=a\times2^2 \\ 12=4a \\ a=\frac{12}{4} \\ a=3 \end{gathered}[/tex]
Substituting the values of a for 3 and b for 1/2, we have the equation as
[tex]\begin{gathered} y=a(b)^x \\ y=3(\frac{1}{2})^x \\ y=3(0.5)^x \end{gathered}[/tex]
Hence the last option is the answer
