what is the exponential equation that goes through (4, 50) and (2, 2) using y=ab^x?

Question

My teacher explained in class but i still don’t really understand please help lol

Answer 1

First, we substitute the coordinates into the equation:

y=ab^x

50=ab^4

2=ab^2

We can divide the first equation by the second equation and get:

25=b^2

(50/2=25, a/a=1, b^4/b^2=b^2)

When we solve for b, and take the square root of both sides, b=5.

Now, we can use our value of b to get our value of a. We will use the equation from the first point:

2=ab^2

2=a(5)^2

2=25a

2/25=a

.08=a

Now we have our values of a and b, we can put it into the equation and get our answer.

y=(.08)(5)^x

y=.4^x

Hope this helps!