Exponential from 2 points

Question

Write an exponential function in the form y=ab^x that goes through points (0,9)and (10,9216)

Answer 1

The best place to start here is with the point (0,9). Since raising any number to the 0 power yields 1, plugging that point into the generic exponential function allows us to solve for the value of a:

y = a*b^x ; 9 = a*b⁰ ; a = 9

Now that we know the value of a, we can use the point (10, 9216) to solve for b:

y = 9*b^x ; 9216 = 9*b¹⁰ ; 1024 = b¹⁰ ; b = 2

Therefore, our exponential function is y = 9*2^x.

Answer 2

(0,9) --> x y=9 when x = 0

9 = a (b^0) = a*1 = a , so a=9 ---> y = 9*b^x

(10,9216) ---> y = 9216 when x = 10

9216 = 9 * b^10

1024 = b^10

2^10 = b^10

b = 2, upon taking log of both sides and dividing by 10

y = 9*2^x

Answer 3

y = ab^x

9 = ab⁰ = a(1) = a

a = 9

9216 = 9b¹⁰

b¹⁰ = 1024

b = 1024^1/10 = 2

b = 2

The function is

y = 9 (2)^x

Test the answer.