Question

What is the exponential regression equation that fits these data? X y 1 3 2 8 3 27 4 85 5 240 6 570 A. Y = 2.93(1.03x) B. Y = 38.73x2 – 168.58x + 158.1 C. Y = 102.54x – 203.4 D. Y = 1.03(2.93x)

Answer 1

Answer:

D) $Y = 1.03(2.93^x)$

Step-by-step explanation:

To Find the exponential regression equation that fits these data, we substitute the value of x into the equation and see if it produces the value of y.

x: 1 2 3 4 5 6

y: 3 8 27 85 240 570

A. Y = 2.93($1.03^x$)

Substituting x = 1 to get

Y = 2.93(1.03) ≅ 3

Substituting x = 2 to get

Y = 2.93($1.03^2$) ≅ 3.1

Option A is wrong

B. Y = 38.73x² – 168.58x + 158.1

Substituting x = 1 to get:

Y = 38.73(1)² – 168.58(1) + 158.1 = 28.25

Therefore option B is wrong

C. Y = $102.54^x - 203.4$

Substituting x = 1 to get:

Y = 102.54 – 203.4 = -100.86

D) $Y = 1.03(2.93^x)$

Substituting x = 1 to get:

$Y = 1.03(2.93^1)=3$

Substituting x = 2 to get:

$Y = 1.03(2.93^2)=8.84$

Substituting x = 3 to get:

$Y = 1.03(2.93^3)=25.9$

Option D is the closest, it is the correct option