Find a formula for the exponential function passing through

Find a formula for the exponential function passing through the points (-1, 3/2) and (3,24)

Solution : Points (-1, 3/2) and (3,24).

Let the exponential function be y = ab^x.

Since the function passing through the points, thus

3/2 = ab^(-1) ...(i) and 24 = ab^3 ....(ii)

Divide equation (ii) by the equation (i), we get

24/(3/2) = ab^3 / ab^-1

or 48/(3) = b^4

or 16 = b^4

or 2^4 = b^4

Thus b = 2.

Now from equation (ii), we have

24 = ab^3

or 24 = a(2)^3

or 24 = a(8)

or a = 3.

Hence y = 3 (2)^x. Ans