Answer:
[tex]y=20(2)^x[/tex]
Step-by-step explanation:
We want to write an exponential function that goes through the points (0, 20) and (6, 1280).
The standard exponential function is given by:
[tex]y=ab^x[/tex]
The point (0, 20) tells us that y = 20 when x = 0. Hence:
[tex]20=a(b)^0[/tex]
Simplify:
[tex]20=a(1)\Rightarrow a=20[/tex]
So, our exponential function is now:
[tex]y=20(b)^x[/tex]
Next, the point (6, 1280) tells us that y = 1280 when x = 6. Thus:
[tex]1280=20(b)^6[/tex]
Solve for b. Divide both sides by 20:
[tex]64=b^6[/tex]
Therefore:
[tex]b=\sqrt[6]{64}=2[/tex]
Hence, our function is:
[tex]y=20(2)^x[/tex]
