SOLUTION: A protected wooded area was stocked with 1500 deer of a certain species in 1995. The deer population in 2010 was found to be 3350 deer. a. Let t be the number of years after 199

Question 773262: A protected wooded area was stocked with 1500 deer of a certain species in 1995. The deer population in 2010 was found to be 3350 deer.
a. Let t be the number of years after 1995. Find the deer population at t=0.
b. Find the growth function that gives the deer population t years after 1995.
c. Predict the deer population in 2020.
d. In what year will the deer population reach 9,000? Give the exact value for t and then use your calculator to approximate t to get the year.
e. Are your answers for parts (c) and (d) consistent with the given population data in you found to the answer in part (b)?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
a) 1500
b) A = P*e^kt
3350 = 1500*e^k*15
2.23 = e^15k
ln(2.23) = 15k
k = ln(2.23) / 15
k = 0.05
A = P*e^0.05t
c) A = 1500*e^0.05*25
A = 1500*2.718^(0.05*25)
A = 5235
d) 9000 = 1500 *e^0.05*t
6 = e^0.05t
ln6 = 0.05t
t = ln6 / 0.05
t = 35.84 years
approx year is 1995 + 35.84 = 2030.84 = 2031
e) A = 1500*e^0.05*15
A = 1500*2.718^0.05*15
A = 3281
approx equal, model is consistent
RELATED QUESTIONS
Suppose that 40 deer are introduced in a protected wilderness area. The population of... (answered by solver91311)

Suppose that 40 deer are introduced in a protected wilderness area. The population of the (answered by ikleyn)

There was a population of 280 deer in a National Park. After a year, the population... (answered by TimothyLamb)

A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will... (answered by robertb)

Here is a word problem I am having difficulty getting started on. I don't have an... (answered by stanbon,richard1234)

A small lake is stocked with a certain species of fish. The fish population is modelled... (answered by ankor@dixie-net.com)

The population of deer in Adrian�s Preserve increases by 6% each year. Which statement... (answered by stanbon,addingup)

A small lake is stocked with a certain species of fish. The fish population is modeled by (answered by ankor@dixie-net.com)

biologist tagged and released 330 deer. A month later she captured 40 deer, 30 of which... (answered by josgarithmetic)