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

$y=10.8^x+19$