College Algebra Prob

Question

Suppose that in a city having a population of 60,000 people the city planners have said that they would like to have a modest population growth of 5% per year. On the other hand, the real estate developers favor a growth rate of 10% per year. With growth of course will come a need for more roads and schools.

a. Let C(t) be the population after t years with the city planners’ growth rate and let D(t) be the population after t years with the developers’ growth rate. Find algebraic formulas for the two functions.

b. If it will take 10 years to build enough roads and schools to accommodate a population of 100,000 people, will either growth plan be acceptable? Write 2 – 3 sentences to support your answer. c. With each growth plan, how many years will it take the population to double?

Answer 1

C(t) = 60000 * (1.05)^t

D(t) = 60000 * 1.1^t

C(10) = 97734

D(10) = 155625

The city planner's is more acceptable.

For the population to double:

2 = 1.05^t vs 2 = 1.1^t

log 2 = t * log 1.05 vs log 2 = t*log1.1

t = log2 / log 1.05 vs t = log 2 / log 1.1

t=14.21 vs t = 7.27