Question

Write an exponential function in the form y = ab" that goes through points (0,7) and (9,3584).

Answer 1

Answer:

Step-by-step explanation:

I'm going to  assume you meant y = ab^x. If this is not correct, leave a comment.

x = 0

y = 7

7 = a * b^0

anything to the zero power is 1

y = a*b^0

y = a*1

7 = a

So far what you have is

y = 7 * b^x

Now let

x = 9

y = 3584  

3584 = 7 * b^9         Divide by 7

3584/7 = b^9

512 = b^9

If you knew how to use logs, that would be the surest way to do this question. However I'm going to make an assumption again and assume that you have not taken those yet.

So the easiest way is to find out what raised to the 9th power will equal 512

Could b = 5?

5^9 = 1 million 9 hundred thousand something. 5 is far too big. Make sure you understand why. 1 million is far greater than 512

So let's try b = 3

3^9 = 19 thousand which is still far too big. 19 thousand something is far larger than 512.

We have just one more number that we can try.

2^9 = 512 and we have it

Answer y = 7*2^x