Question

question 5 of 10
what is the exponential regression equation that fits these data?

x	y
-4	0.025
-3	0.075
-2	0.25
-1	0.70
0	3
1	8
2	20
3	60
4	160

a. y = 4.90x² + 14.44x - 4.69
b. y = 2.26 · 3.02^x
c. y = 3.02 · 2.26^x
d. y = 2.01 · 3.80^x

Explanation:

Step1: Recall exponential regression form

The general form of an exponential regression equation is $y = ab^{x}$, where $a$ and $b$ are constants.

Step2: Use the point $x = 0$

When $x = 0$, $y=a\times b^{0}=a$. From the table, when $x = 0$, $y = 3$, so $a = 3$.

Step3: Test other points with approximate values

We can take another point, say $x = 1,y = 8$. Substituting $a = 3$ into $y=ab^{x}$, we get $8=3\times b^{1}$, so $b=\frac{8}{3}\approx2.67$. Among the given options, the closest form to our - estimated values is when we consider the general exponential - form. Option C: $y = 3.02\times2.26^{x}$ has $a\approx3$ and $b\approx2.26$ which is relatively close to our estimated values.

Answer:

C. $y = 3.02\cdot2.26^{x}$