A country's population, in millions, is given by the exponential model P = 78.2e0.047t, where t represents years after 2000. After how many years will the country have a population of 210 million? (Round answer to the nearest tenth.)
A)
12.0 years
B)
21.0 years
C)
29.8 years
D)
37.8 years

Question

A country's population, in millions, is given by the exponential model P = 78.2e0.047t, where t represents years after 2000. After how many years will the country have a population of 210 million? (Round answer to the nearest tenth.)
A)
12.0 years	
B)
21.0 years	
C)
29.8 years	
D)
37.8 years

anonymous · Answer

so, we need to solve for Time t

$$P(t) = 78.2* e^{0.047 t}$$

Now, let P(t) = 210 millions:

$$210 = 78.2* e^{0.047 t}$$ ; divide both sides by 78.2 you get:

$$2.685242 = e^{0.047 t}$$; now take the natural log ( ln ) of both sides:

$$ln 2.685242 = ln e^{0.047 t}$$ ; which is equal to:

$$ln 2.685242 = {0.047 t}$$ because ln e = 1, and so :

t = 21.017 years.

therefore the answer is B) 21 years.

anything you don't understand let me know!

anonymous · Answer

wow thank you i used to be good at this but i completely forgot it.