exponential solving for 2 points

Question

write an exponential equation y=a(b^(x)) for a graph that passes through the points (0,7) and (-1,3.5).

Answer 1

Using the first point:

y=a(b^x)

7=a(b⁰)

7=a(1)

7=a

Using the second point and the a value we just found:

3.5=7(b^-1)

Divide both sides by 7 and simplify

3.5/7=7(b^-1)/7

1/2=b^-1

1/2=1/b

2=b

Bringing these values together the equation is:

y=7(2^x)