Answer:
t = 15.18 years old
B(t) = 6,320*e^-0.1t*( 1 - 0.93*e^ -0.095t )^3]
t = 13.426 years
Step-by-step explanation:
The complete question is given as follows:
Given:
- The number of fish in population according to bio-mass:
N = 1000*e^-0.1t
- The weight of each fish is given by:
w = 6.32*( 1 - 0.93*e^ -0.095t )^3
w : Weight in pounds,
t : Age in years
Find:
- If a fish weighs 3 pounds, how old is it?
- Find the Formula for biomass B(t) = w*N , and graph the function.
- At what age is the bio-mass largest?
Solution:
- Using the weight formula and set w = 3 , we have:
3 = 6.32*( 1 - 0.93*e^ -0.095t )^3
e^ -0.095t = (1 - ∛(3/6.32))/0.93
-0.095*t = Ln | (1 - ∛(3/6.32)) / 0.93 |
t = -Ln | (1 - ∛(3/6.32)) / 0.93 | / 0.095
t = 15.18 years old
- The Bio-mass function is given by the product of total number N fishes and the weight of each fish w.
B(t) = [ 1000*e^-0.1t ]*[6.32*( 1 - 0.93*e^ -0.095t )^3]
B(t) = 6,320*e^-0.1t*( 1 - 0.93*e^ -0.095t )^3]
- The graph is plotted as attached.
- From the plotted graph the function B(t) maximizes when t = 13.426 years
