Answer the problem. Show solution please!

Question

The population of a city is currently 50,000. If it is expected to double every 15 years, when will the population reach 140,000 people?

Answer 1

We want to use the formula

 

P = P₀e^kt

 

where:

P = population in thousands

t = number of years

P₀ = the initial population

 

Find the value of k.  When t=15, P=100

 

100 = 50e^15k

 

Solving for k,

 

2 = e^15k

 

 

Log both sides of the equation.

 

ln(2) = 15klne

 

ln2 = 15k

 

ln(2) / 15 = k

 

0.046 = k

 

 

Your formula is then

 

P(t) = 50e^0.046t

 

 

Use it to find the value of t when P(t) is 140.