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In a field study, a scientist was predicting the insect population. The initial amount of insects in the area was 15,000. The scientist found the rate to be 15%; however, the scientist did not record if this was a growth rate or a decline rate.

a. If the rate is a growth rate, what would be the estimated population in 6 years? Show all of your work.
b. If the rate is a decline rate, what would be the estimated population in 6 years? Show all of your work.

Answer :

Abidemiokingo

The estimated population, if the rate is a growth rate is 34696 populations

The estimated population, if the rate is a decline rate is 5657 populations

Exponential functions

The standard exponential equation is expressed as [tex]y = ab^x[/tex]

where;

  • a is the intercept
  • b is the growth rate
  • x is the time taken

If the initial population is 15,000 with a rate of 15%, then;

a) If the rate is a growth rate, the estimated population will be expressed as;

[tex]y = 15000(1+0.15)^{6}\\y=15000(1.15)^6\\y = 15000(2.313)\\y \approx 34,696[/tex]

The estimated population, if the rate is a decline rate is 34696 populations

b) If the rate is a decline rate, the estimated population will be expressed as;

[tex]y = 15000(1-0.15)^{6}\\y=15000(0.85)^6\\y = 15000(0.37715)\\y \approx 5,657[/tex]

The estimated population, if the rate is a decline rate is 5657 populations

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