ive tried but i dont know what to do precalculus hw

Question

An exponential function  passes through the points (0, 4) and (2, 36). What are the values of  and ? 

 =  and

  = 

Answer 1

Hello Cristal,

We know this exponential function will be of the form y = a * b^x.

The first thing I did was plug in the point (0,4). This gives us 4 = a * b⁰.

Any number raised to a power of zero is 1, so b⁰ is equal to 1. We are left with 4 = a.

Now that we know a = 4, we can plug this in, as well as the other point, (2,36), and solve for b.

This gives us 36 = 4 * b². We can divide both sides by 4 to get 9 = b².

This means b is equal to ±3, however b for an exponential function can only be any positive real number excluding 1. This means that we can forget the negative value, and our answer is b = 3.

The final equation would look like y = 4 * 3^x.

Good luck on your homework!

Katie