Question

Identify the initial amount a and the growth factor b in the exponential function A(x)=680*4.3^x

Answer 1

Hey Jack!
So the initial amount corresponds to when x=0.

Answer 2

Remember what happens when you raise something to the 0th power?\[\Large\rm 4.3^0=1\]It just gives us 1!

Answer 3

\[\Large\rm A(x)=680*4.3^x\]\[\Large\rm A(0)=680*4.3^0\]\[\Large\rm A(0)=680*1\]So this gives us our `amount` at x=0. Our starting amount.

Answer 4

If that's too confusing, you can instead relate your function to the general form:\[\Large\rm f(x)=\color{royalblue}{a}(\color{orangered}{b})^x\]And we would relate this to the function they gave us:\[\Large\rm A(x)=\color{royalblue}{680}(\color{orangered}{4.3})^x\]

Answer 5

Thanks.