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

Click here to see ALL problems on logarithm

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