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Sagot :
Answer:
See below ~
Step-by-step explanation:
What is the rat population in 1993?
⇒ Number of years since = 0 ⇒ t = 0
⇒ Apply in the formula
⇒ n(0) = 73e^(0.02 × 0)
⇒ n(0) = 73e⁰
⇒ n(0) = 73,000,000 rats
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What does the model predict the rat population was in the year 2009?
⇒ Number of years since 1993 : 2009 - 1993 = 16 ⇒ t = 16
⇒ Applying in the formula
⇒ n(16) = 73e^(0.02 × 16)
⇒ n(16) = 73e^(0.32)
⇒ n(16) = 73 × 1.37712776 × 10⁶
⇒ n(16) = 100.530326 x 10⁶
⇒ n(16) = 100,530,326 rats
Answer:
Given function:
[tex]\large \text{$ n(t)=73e^{0.02t} $}[/tex]
where:
- t is the number of years since 1993
- n(t) is the rat population measured in millions
To calculate the rat population in 1993, substitute [tex]t = 0[/tex] into the function:
[tex]\large \begin{aligned}\implies n(0) & =73e^{0.02(0)}\\& = 73 \cdot 1\\& = 73 \sf \: million\end{aligned}[/tex]
To calculate a prediction of the rat population in 2009, first determine the value of t by subtracting the initial year of 1993 from the given year of 2009:
[tex]\large \text{$ \implies t=2009-1993=16 $}[/tex]
Substituting the found value of t into the function to find the predicted number of rats in 2009:
[tex]\large \begin{aligned}\implies n(16) & =73e^{0.02(16)}\\& = 73e^{0.32}\\& = 100.5303268...\\ & = 100.5 \sf \: million\:(1\:dp)\end{aligned}[/tex]
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