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.
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
1 answer