Use the exponential regression equation that best fits the data (2, 7), (3,10), (5, 50), and (8, 415) to estimate the value of y when x =c7.
A. 47.32
B. 61.56
C. 99.87
D. 200.64
The exponential regression equation can be represented as y = ab^x, where a is a constant and b is the exponential growth factor.
To find the values of a and b, we need to use the given data points.
Using the first data point (2, 7):
7 = ab^2
Using the second data point (3, 10):
10 = ab^3
From the first equation, we can solve for a:
a = 7/b^2
Substituting this value of a into the second equation, we get:
10 = (7/b^2)b^3
10 = 7b
Solving for b, we find:
b = 10/7
Substituting this value of b into the first equation, we get:
7 = a(10/7)^2
7 = 100a/49
a = 49/100
So the exponential regression equation is: y = (49/100)(10/7)^x
To estimate the value of y when x = c7:
y = (49/100)(10/7)^(c7)
We can calculate this estimate using a calculator or spreadsheet.
Using a calculator, we can enter: (49/100)(10/7)^7
The estimated value of y is approximately 99.87042872.
Therefore, the correct answer is C. 99.87.