Question

write an exponential equation in the form y = ab* whose graph passes through points (-3, 24) and (-2, 12).

Answer 1

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

`y=a(b)^x`

Now we will substitute -3 for x and 24 for y, we have

`24=a(b)^(-3)`

Also substituting -2 for x and 12 for y, we have

`12=a(b)^(-2)`

Dividing equation 2 by equation 1, we have

`\begin{gathered} (12)/(24)=(a(b)^(-2))/(a(b)^(-3)) \\ (1)/(2)=b^(-2-(-3)) \\ (1)/(2)=b^(-2+3) \\ (1)/(2)=b \\ b=(1)/(2) \end{gathered}`

Now substitute this value of b into equation 2, we have

`\begin{gathered} 12=a(b)^(-2) \\ 12=a((1)/(2))^(-2) \\ 12=a*(2^(-1))^(-2) \\ 12=a*2^2 \\ 12=4a \\ a=(12)/(4) \\ a=3 \end{gathered}`

Substituting the values of a for 3 and b for 1/2, we have the equation as

`\begin{gathered} y=a(b)^x \\ y=3((1)/(2))^x \\ y=3(0.5)^x \end{gathered}`

Hence the last option is the answer