Question

The sketch shows a curve with equation y=ab^x where a and b are constants and b>0.

The curve passes through the points (0,3) and (2,12).

Calculate the value of a and b.

Thank you.

Answer 1

b^0 = 1, so a=3

Now you know that 3b^2 = 12

I expect you can find b now ...

Answer 2

sub in the two points to set up two equations

for (0,3)
3 = a b^0, but b^0 = 1
so a = 3

for (2,12)
12 = 3 b^2
4 = b^2
b = ± 2, but we need b> 0

a = 3 , b = 2 ---> y = 3 (2)^x