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26.03.2020 •
Mathematics
An initial population of fish is introduced into a lake. This fish population grows according to a continuous exponential growth model. There are fish in the lake after years. (a)Let be the time (in years) since the initial population is introduced, and let be the number of fish at time . Write a formula relating to . Use exact expressions to fill in the missing parts of the formula. Do not use approximations. (b)How many fish are there years after the initial population is introduced
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Ответ:
Given question is incomplete; find the complete question,
An initial population of 80 fish is introduced into a lake. This fish population grows according to a continuous exponential growth model. There are 216 the lake after 12 years.
(a) Let t be the time (in years) since the initial population is introduced and let y be the number of fish at time t. Write a formula relating y to t. Use exact expressions to fill in the missing parts of the formula. Do not use approximations.
(b) How many fish are there 3 years after the initial population is......? Do not round any intermediate computations, and round your answer to the nearest whole number.
Expression for the population growth will be,
and there will be 103 fishes in the pond after 3 years.
(a). Given in the question,
Initial population of fish = 80Final population of fish = 216Time taken to reach the final population = 12 yearsExpression for the population after time 't' is given by,
Here,
Initial population
Expression for the population,
Expression for the population growth will be,
(b). For t = 3 years,
Therefore, expression for the population growth will be
and population of fish after 3 years will be nearly 103.
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Ответ:
(a)![y=80e^{\dfrac{ln(2.7)t}{12}](/tpl/images/0566/0426/85328.png)
(b)301
Step-by-step explanation:
By the exponential population model,the population P(t) at any time t is given as:
where
is the initial population.
P(12)=y=216 at t=12 years
Taking the natural logarithm of both sides
12r=ln(2.7)
(b) After 16 years
At t=16
After 16 years, there are approximately 301 fishes in the lake.
Ответ:
J
Step-by-step explanation: