3.1 sections of work

Question

Find the Functions of the form F(x) = ca^x that contain two given graphs: Please provide a video or explain it to me how you gotten the answer?

1.) (0,1), (2,16) ---------------> Answer: 4^x

2.) (0,3) (2,12) ---------------> Answer: 3*2^x

Answer 1

You just need to use the property of power: a⁰=1 (valid for any non-zero a)

Take the first point (0,1). Another words, when x=0 F(0) = ca⁰ =c=1 Therefore F(x)=a^x

Then take the 2nd point (2,16) That tells you that when x=2 F(1)=a²=16 From here IaI=4 (one solution is a=4 (another solution a=-4 makes no difference here b/c F uses a² )

So, F(x)=1_*4^x=4^x

The second problem is solved the same way

Answer 2

Using the standard form of the equation: y=c(a)^x

Plug in the first point, the one with the 0.

1=c(a)⁰ Anything raised to the zero power is 1 so this allows you to solve for c

c=1

Next, use the second point and the c value you just found

16=a² Take the square root of both sides

a=4

Put both of these together for the equation

y=(4)^x