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Q. 10

Expert-verifiedFound in: Page 797

Book edition
4th

Author(s)
David Moore,Daren Starnes,Dan Yates

Pages
809 pages

ISBN
9781319113339

We record data on the population of a particular country from $1960$ to $2010$. A scatterplot reveals a clear curved relationship between population and year. However, a different scatterplot reveals a strong linear relationship between the logarithm (base 10) of the population and the year. The least-squares regression line for the transformed data is,

log ( population) $=-13.5+0.01$ (years).

Based on this equation, the population of the country in the year 2020 should be about

(a) $6.7$

(b) $812$

(c) $5,000,000$

(d) $6,700,000$

(e) $8,120,000$.

The population of the country in the 2020 should be about $5,000,000$. The correct option is (c).

The population of the country in the year 2020 should be about log (population)$=-13.5+0.01$.

Putting the year with 2020 :

log (population) $=-13.5+0.01\left(2020\right)$

$=6.7$

Taking the exponential

Population $={10}^{6.7}$

Evaluate $=5011872$

$=5000000$

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