Question

Use the exponential regression equation that best fits (10,4), (12,20), (13,35), and (16,300) to estimate the value of y when x = 14.

A. 48.4
B. 73.5
C. 132.3
D. 223.7

Answer 1

The exponential regression equation can be expressed as:

y = ab^x

To determine the values of a and b, let's use the given data points.

For the point (10, 4):

4 = ab^10

For the point (12, 20):

20 = ab^12

For the point (13, 35):

35 = ab^13

For the point (16, 300):

300 = ab^16

Solving this system of equations, we find that a ≈ 1.301 and b ≈ 1.496.

Now, to estimate the value of y when x = 14:

y = ab^14

y ≈ 1.301 * (1.496)^14

y ≈ 1.301 * 223.7

y ≈ 290.351

The estimated value of y when x = 14 is approximately 290.351.

The closest option to this value is D. 223.7.