Respuesta :
The population of fish first exceed the capacity of the lake will be 2046. Then the correct option is C.
What is an exponent?
Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)Ë£
The population of a certain fish species can be modeled using the equation
[tex]\rm P(t)= 50 \ e^{0.15t}[/tex]
where t is the number of years after 2018.
A particular lake can accommodate at most 3,500 of this fish species.
Based on the model, the year in which population of fish first exceed the capacity of the lake 3,500 will be
[tex]\rm 3500= 50 \ e^{0.15t}\\\\70 \ \ \ = e^{0.15t}[/tex]
Taking log on both sides, we have
ln 70 = 0.15t ln e
4.248 = 0.15 t
t = 28.32 ≈ 28 years
Then the year will be
⇒ 2018 + 28
⇒ 2046
The population of fish first exceed the capacity of the lake will be 2046.
Then the correct option is C.
More about the exponent link is given below.
https://brainly.com/question/5497425
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