Trout Population Decline Calculation
The image presents a math problem that involves the function \( N(t) = 15,000 \times (0.95)^t \), which represents the number of trout after t years. The question asks what will happen to the trout population five years after they were released into the Kootenai River.
To determine the impact on the population after 5 years, you would substitute t = 5 into the function \( N(t) \):
\( N(5) = 15,000 \times (0.95)^5 \)
Now we calculate \( (0.95)^5 \) and then multiply the result by 15,000:
\( (0.95)^5 ≈ 0.7738 \) (rounded to four decimal places)
Then multiply that by 15,000 to see the number of trout:
\( 15,000 \times 0.7738 ≈ 11,607 \)
Originally, there were 15,000 trout. After 5 years, there would be approximately 11,607 trout if we use the estimated value.
Now to find the change in population:
Initial number of trout: 15,000
Number of trout after 5 years: 11,607
Decrease in trout: 15,000 - 11,607 = 3,393
The closest answer to this number is:
(B) It will decrease by about 3,200.
So the answer is (B) the population will decrease by about 3,200.
