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I am Lyosha [343]
3 years ago
15

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 t

he 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
Mathematics
1 answer:
djyliett [7]3 years ago
7 0

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

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.

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