Question

Find the starting value and the base for the exponential function f(x)=kb^x that passes through the two points:(0,2000) and (2,20).The starting value k is: AnswerThe base b is: Answer

Answer 1

$\begin{gathered} \text{Given} \\ f(x)=kb^x \\ \text{Points }(0,2000)\text{ and }(2,20) \end{gathered}$

Use point (0,2000) to solve for k

$\begin{gathered} \Big(x,f(x)\Big)=(0,2000) \\ \\ f(x)=kb^x \\ 2000=kb^0 \\ 2000=k\cdot1 \\ k=2000 \end{gathered}$

Use point (2,20) and k = 2000 to solve for b

$\begin{gathered} \Big{(}x,f(x)\Big{)}=(2,20) \\ k=2000 \\ \\ f(x)=kb^x \\ 20=2000\cdot b^2 \\ b^2=\frac{20}{2000} \\ b^2=\frac{1}{100} \\ \sqrt[]{b^2}=\sqrt[]{\frac{1}{100}} \\ b=\frac{1}{10} \end{gathered}$