How to find an exponential equation?

Question

(1,7.5) and (3, 16.875)

Thanks!

Answer 1

y=a*b^x

7.5=a*b¹           equation 1

16.875=a*b³     equation 2

 

If we divide the second equation by the first, we have:

16.875/7.5=(a/a)*(b³/b¹)

2.25=b²

b=√2.25

b=1.5

 

Plug b into the first equation:

7.5=a*(1.5)¹

a=5

 

Check your solutions using the second equation:

16.875=5*(1.5³)

16.875*16.875

 

a=5 and b=1.5

y=5*(1.5)^x  is our equation