Question

question 11 of 13 which of the following exponential regression equations best fits the data shown below?

x	-4	-3	-2	-1	0	1	2	3	4
y	0.05	0.20	0.75	2.25	10	30	100	350	1250

a. y = 10.84·1.77^x
b. y = 8.46·3.51^x
c. y = 5.32·2.23^x
d. y = 3.14·4.98^x

Explanation:

Step1: Recall exponential regression form

The general form of an exponential regression equation is $y = ab^{x}$, where $a$ is the y - intercept (value of $y$ when $x = 0$) and $b$ is the base of the exponential function.

Step2: Check y - intercept

When $x = 0$, from the data table $y=10$. We check the y - intercepts of the given equations:

• For option A: When $x = 0$, $y=10.84\times1.77^{0}=10.84$.
• For option B: When $x = 0$, $y = 8.46\times3.51^{0}=8.46$.
• For option C: When $x = 0$, $y=5.32\times2.23^{0}=5.32$.
• For option D: When $x = 0$, $y = 3.14\times4.98^{0}=3.14$.

The value closest to the actual $y$ - value ($y = 10$ when $x = 0$) among the options is in option A.

Answer:

A. $y = 10.84\cdot1.77^{x}$