1. The population of a southern city follows the Natural Growth Model. If the po

Question

1. The population of a southern city follows the Natural Growth Model. If the population doubled in size over a 2-year period and the current population is 10,000.

a) Find an expression of the population after t years.

c. What will be the population two years from now?

d. When will the population reach 100,000 people?

e. Find the rate of growth after 4 years. Hint: you will need to think about the graphical representation of a derivative.

f. Find the rate of growth after 6 years. Include units in your answer. Hint: you will need to think about the graphical representation of a derivative.

g. Is the population growing faster after 4 years or 6 years?

2. The population of a colony of mosquitoes obeys the law of natural growth.

a. If there are 1,000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after 3 days?
b. How long is it until there are 10,000 mosquitoes?
c. Find the rate of growth after 7 days. Include units in your answer.

Explanation / Answer

We are allowed to do 1 question at a time. Post again for second question.

N=Ae^kT where A is the initial population and k is a constant to be determined.

(a) N=1000e^kT
Substitute T=1 and N=1800.
1800=1000e^k
1·8=e^k
ln1·8=k
k=0·588
N=1000e^(0·588T)
So after 3 days the population is:
1000e^(0·588*3) = 5832

(b) Substitute N=10000 into N=1000e^(0·588T)
10000=1000e^(0·588T)
10=e^(0·588T)
ln(10)=0.588T
2·303=0·588T
T=3·92
There are 10000 mosquitoes after 3·92 days

c) N=1000e^(0·588 * 7)

N = 61313.5

Growth rate = (61313.5 - 1000) * 100/1000 = 6031.35%

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.