Find the formula for an exponential function that passes through the two points given. (x, y) = (2, 1.2) and (x, y) = (5, 9.6)

Answer 1

a(b^2) = 1.2

a(b^5) = 9.6

divide 2nd by 1st equation to get

b^3 = 9.6/1.2 = 8

b = cube root of 8 = 2 (ignore the other two imaginary cubes roots)

4a = 1.2

a = 1.2/4 = .3

y = .3(2^x) is the exponential equation through the two given points

Answer 2

An exponential function has the general form:

y=ab^x

Where a is the initial value and b is the base of the exponential. To find the formula for the function passing through the points (2, 1.2) and (5, 9.6):

1.2 = ab²

9.6 = ab⁵

(9.6 / 1.2) = (ab⁵ / ab²)

8 = b^5-2

8 = b³

b = ³√8 = 2

Once solving for b, substitute b = 2 into the original equations.

1.2 = ab²

1.2 = a(2)²

1.2 = 4a

a = (1.2 / 4) = 0.3

The exponential function is:

y = 0.3(2^x)