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The linearized regression equation for an exponential data set is log ŷ = 0.14x + 0.4, where x is the number of years and y is the population. What is the predicted population when x = 15? Round your answer to the nearest whole number.

A.3
B.126
C.316
D.9537

User Dza
by
7.3k points

1 Answer

5 votes

Option C:
316 is the predicted population when
x=15

Step-by-step explanation:

The regression equation for an exponential data is
\log y=0.14x+0.4

Where x is the number of years and

y is the population

We need to determine the predicted population when
x=15

The population x can be determined by substituting
x=15 in the equation
\log y=0.14x+0.4

Thus, we have,


\log y=0.14(15)+0.4


\log y=2.1+0.4


\log y=2.5

Using the logarithmic definition
\log _(a)(b)=c then
b=a^(c)


\log _(10)(y)=2.5 \Rightarrow y=10^(2.5)


y=316.22776 \ldots

Rounding off to the nearest whole number, we get,


y=316

Thus, the predicted population when
x=15 is 316

Hence, Option C is the correct answer.

User VerteXVaaR
by
6.6k points