what is the exponential model y=a b^x for the graph that passes through the point (3,5) and (4,10)

Question

need asap

Answer 1

5 = a b^3        10 = a b^4

solving the first one, you get a = 5/(b^3)

substituting that into the second equation

10 = 5/(b^3) b^4

10 = 5b

b=2

5=a 2^3

5=8a

a=5/8

y= (5/8) 2^x

 

check with the second point

10=(5/8) 2^4

10=(5/8) 16

10=10

 

y= (5/8) 2^x is the exponential model.

Answer 2

y = ab^x

 

You need to solve for a and b using the 2 given points.

 

5 = ab³

10 = ab⁴

 

Divide bottom equation by top equation and get

 

b = 2

 

y = a 2^x

 

Now use either point to find a.

 

5 = a 2³ = 8a

 

a = 5/8

 

y = (5/8)(2^x)