Question

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The rat population in a major metropolitan city is given by the formula n(t)=89e^0.02t where t is measured in years since 1992 and n(t) is measured in millions

What was the rat population in 1992?

What does the model predict the rat population was in the year 2003?

Answer 1

See below ~

Step-by-step explanation:

What was the rat population in 1992?

⇒ t represents the years after 1992

⇒ So, in 1992, t = 0

⇒ Apply in the formula

⇒ n(0) = 89e^(0.02 × 0)

⇒ n(0) = 89e⁰

⇒ n(0) = 89,000,000

The rat population in 1992 was 89,000,000.

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What does the model predict the rat population was in the year 2003?

⇒ Number of years after 1992 : 2003 - 1992 = 11

⇒ Substitute for t in the formula

⇒ n(11) = 89e^(0.02 × 11)

⇒ n(11) = 89e^(0.22)

⇒ n(11) = 89 × 1.24607673

⇒ n(11) = 110,900,829 rats

The model predicts that in the year 2003 there will be a rat population of 110,900,829 rats.

Answer 2

(a) 89,000,000 rats

(b) 110,900,829 rats

Step-by-step explanation:

Given equation:

• n(t)=89e^0.02t

To find the initial population (1992):

insert t = 0

• n(0) = 89e^0.02(0) = 89 million ≈ 89,000,000

To find the rat population in 2003 (after 11 years):

insert t = 11

• n(11) = 89e^0.02(11) = 89e^0.22 ≈ 110,900,829