The population of mosquitoes in a swamp is estimated over the course of twenty weeks, as shown in the table. Time(weeks) Population 0 100 5 1,000 10 10,000 15 100,000 20 1,000,000 Which of the following best describes the relationship between time and the estimated population of mosquitoes during the twenty weeks?

Correct Answer is : Exponential growth

SAT Mathematics Practice Test 4

Question : 33 of 58

Marks: +1, -0

The population of mosquitoes in a swamp is estimated over the course of twenty weeks, as shown in the table.

Time(weeks)	Population
0	100
5	1,000
10	10,000
15	100,000
20	1,000,000

Which of the following best describes the relationship between time and the estimated population of mosquitoes during the twenty weeks?

Increasing linear
Decreasing linear
Exponential growth
Exponential decay

Validate

Solution:

The mosquito population starts at 100 in week 0 and then is multiplied by a factor of 10 every 5 weeks. Thus, if

P(t)

is the mosquito population after t weeks, then based on the table,

P(t)=100(10)^{1/3}

which indicates an exponential growth relationship.
Choices A, B, and D are incorrect and may be the result of an incorrect interpretation of the relationship or errors in modeling the relationship

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