Answer:
Population = 691.83 (rounded = 692)
Step-by-step explanation:
The equation is:
[tex]Logy=0.23x+0.08[/tex]
When there is no base written with log, we assume "base 10", so we can say:
[tex]Log_{10}y=0.23x+0.08[/tex]
Now, we need to find the population (y) when x = 12. Lets plug in 12 into x:
[tex]Log_{10}y=0.23x+0.08\\Log_{10}y=0.23(12)+0.08\\Log_{10}y=2.84[/tex]
Now, we change to exponential form by using the formula shown below:
[tex]Log_{10}x=b\\10^b=x[/tex]
So, we have:
[tex]Log_{10}y=2.84\\y=10^{2.84}[/tex]
Evaluate using calculator to get:
[tex]y=10^{2.84}\\y=691.83[/tex]
The population after 12 years, would be 691.83, rounded, 692
