The rate of growth of a fish population was modeled by the equation 90,000e-0.6t (1 + 5e−0.6t)², where t is measured in years since 2000 and G in kilograms per year. Write an integral to find the change in the population predicted between 2000 and 2020. 90,000e-0.6t 20 +5e-0.6t 10 G(t) = -30000 -0.6t) 2 dt 1 Find a substitution and apply it to rewrite the integrand in the form u² -12 1 + 5e · ) ( ( ) du du. If the biomass was 15,000 kg in the year 2000, what is the predicted biomass (in kg) for the year 2020? (Round your answer to the nearest whole number.) X kg

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
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The rate of growth of a fish population was modeled by the equation
-0.6t
10
G(t) =
where t is measured in years since 2000 and G in kilograms per year.
Write an integral to find the change in the population predicted between 2000 and 2020.
20
90,000e-0.6t
+5e-0.6t
90,000e
(1 + +5e-0.6t) ²,
-30000
-0.6t) 2
dt
1
Find a substitution and apply it to rewrite the integrand in the form
U²
-12
1 + 5e
) (+) ₁
du
du.
If the biomass was 15,000 kg in the year 2000, what is the predicted biomass (in kg) for the year 2020? (Round your answer to the nearest whole number.)
X kg
Transcribed Image Text:The rate of growth of a fish population was modeled by the equation -0.6t 10 G(t) = where t is measured in years since 2000 and G in kilograms per year. Write an integral to find the change in the population predicted between 2000 and 2020. 20 90,000e-0.6t +5e-0.6t 90,000e (1 + +5e-0.6t) ², -30000 -0.6t) 2 dt 1 Find a substitution and apply it to rewrite the integrand in the form U² -12 1 + 5e ) (+) ₁ du du. If the biomass was 15,000 kg in the year 2000, what is the predicted biomass (in kg) for the year 2020? (Round your answer to the nearest whole number.) X kg
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