Question

the linearized regression equation for an exponential data set is log y=0.23 + 0,08, where x is the number of years and y is the population. what is the predicted population when x=12?

Answer 1

Answer:

Population = 691.83 (rounded = 692)

Step-by-step explanation:

The equation is:

$Logy=0.23x+0.08$

When there is no base written with log, we assume "base 10", so we can say:

$Log_{10}y=0.23x+0.08$

Now, we need to find the population (y) when x = 12. Lets plug in 12 into x:

$Log_{10}y=0.23x+0.08\\Log_{10}y=0.23(12)+0.08\\Log_{10}y=2.84$

Now, we change to exponential form by using the formula shown below:

$Log_{10}x=b\\10^b=x$

So, we have:

$Log_{10}y=2.84\\y=10^{2.84}$

Evaluate using calculator to get:

$y=10^{2.84}\\y=691.83$

The population after 12 years, would be 691.83, rounded, 692