College Algebra Question

Question

The population of a certain town in the year 2000 was 250 million and the population growth rate is .55% per year. Use the population model P(t)=P₀(t+r)^t  to find the year when the population reaches 350 million. (Round you answer to the nearest year).

Answer 1

I think the population model should be P(t) = P₀(1+r)^t 

 

P₀ = 250 million

r = 0.55% = 0.0055

t = years since 2000 

 

Set P(t) = 350 million and solve for t

 

350 million = (250 million)(1.0055)^t

(1.0055)^t = 1.4

 

Take the logarithm of both sides.  I prefer the natural logarithm ln but if you're more comfortable with base 10 logarithms they will work just as well 

 

ln(1.0055^t) = ln(1.4)

t*ln(1.0055) = ln(1.4)

t = ln(1.4) / ln(1.0055) ≅ 61.34 years 

 

So the population will reach 350 million in 2061