The population (in millions) of a certain country can be approximated by the function P(x)=50(1.03)^x , where x is the number of years since 2000. In which year will the population reach 100 million? Hint: An answer such as 2002.4 would represent the year 2002.

Question

The population (in millions) of a certain country can be approximated by the function P(x)=50(1.03)^x    , where x is the number of years since 2000. In which year will the population reach 100 million? Hint: An answer such as 2002.4 would represent the year 2002.

wolf1728 · Answer

I think more explanation is needed.
The equation (for zero years) generates the number 50.
So, the population in the year 2000 is 50 million?

wolf1728 · Answer

P(x)=50(1.03)^x
When population = 100 million formula is:
P(x)=100(1.03)^x
where P(x) would equal 100
100 / 50 = (1.03)^x
Taking logs of both sides:
log (100) -log(50) = x * log (1.03)
2 - 1.6989700043 = x * 0.0128372247
0.3010299957 / 0.0128372247 = x
= 23.4497722504 years
So, 23.4497722504 years after the year 2000, the population will be 100 million.
So the answer is the year 2023 around the middle of May.