Question

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

Answer 1

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.