A protected area was stocked with 1500 deer of a certain species in 1995. The deer population in 2010 was found to be 3350 deer. Let t be the number of years after 1195. Find the deer population at t=3
Assuming a constant % growth rate,
P(t) = 1500 e^kt
P(15) = 3350, so
1500 e^15k = 3350
k = 1/15 ln(3350/1500) = .0536
P(3) = 1500 e^(.0536*3) = 1762
To find the deer population at t = 3, we can use the information given and calculate the average annual growth rate of the deer population.
Given:
- The deer population in 1995 was 1500 deer.
- The deer population in 2010 was 3350 deer.
We know that there are 15 years between 1995 and 2010 (2010 - 1995 = 15). So, the average annual growth rate can be calculated as:
Average annual growth rate = (Final population - Initial population) / Number of years
= (3350 - 1500) / 15
= 1850 / 15
= 123.33 (rounded to two decimal places)
Now, let's calculate the deer population at t = 3, which means 3 years after 1995.
Deer population at t = Initial population + (Average annual growth rate * Number of years)
= 1500 + (123.33 * 3)
= 1500 + 369.99
= 1869.99 (rounded to two decimal places)
Therefore, the deer population at t = 3 would be approximately 1869.99 deer.