Question

Write an exponential function in the form y(0, 20) and (3, 1280).abl that goes through points

Answer 1

the general form of the exponential function is

`y=a^x+b`

first replace (0,20)

`\begin{gathered} 20=a^0+b \\ 20=1+b \\ b=20-1=19 \end{gathered}`

for now, the formula is

`y=a^x+19`

now, replace (3,1280)

`\begin{gathered} y=a^x+19 \\ 1280=a^3+19 \\ a^3=1280-19 \\ a^3=1261 \end{gathered}`
`a=\sqrt[3]{1261}=10.8`

so, the exponential function is

`y=10.8^x+19`