SOLUTION: Please help me all my answers was wrong and I tried it many times. Show all steps. The population of rabbits in a national forest is modeled by the formula: p=12,300+1000In(t+1)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help me all my answers was wrong and I tried it many times. Show all steps. The population of rabbits in a national forest is modeled by the formula: p=12,300+1000In(t+1)      Log On


   

Question 998793: Please help me all my answers was wrong and I tried it many times. Show all steps.
The population of rabbits in a national forest is modeled by the formula: p=12,300+1000In(t+1) where (t) is the number of years from the present.
A) How many rabbits are in he forest now? my answer is 214
B) How many rabbits will be in the forest 1 year from now? my was 332
C) How many years will it take for the rabbit population to reach 15,000? I had 4.7years
The population of foxes in the same forest is modeled by the formula:
P=400+(50)In(90t+1).
D) When the population of foxes is equal to 5% of the population of rabbits, the system is considered to be out of ecological balance. In how many years will the system be out of balance? my answer was 12.5years
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
A) How many rabbits are in he forest now? my answer is 214
t=0;
p=12300%2B1000%2Aln%280%2B1%29
12300%2B1000%2Aln%281%29
1230%2B1000%2A0
12300

B) How many rabbits will be in the forest 1 year from now? my was 332
t=1;
p=12300%2B1000%2Aln%281%2B1%29
p=12300%2B1000%2Aln%282%29
p=13000

C) How many years will it take for the rabbit population to reach 15,000? I had 4.7years
p=15000=12300%2B1000%2Aln%28t%2B1%29
15000-12300=1000%2Aln%28t%2B1%29
2700=1000%2Aln%28t%2B1%29
10%2Aln%28t%2B1%29=27
ln%28t%2B1%29=2.7
e%5E%282.7%29=t%2B1
highlight_green%28t=-1%2Be%5E%282.7%29%29
highlight%28t=13.9%29


--
Question part D asks for a time for a certain comparison between the fox and the rabbit populations. For what value t will foxes be 5% of rabbits?

Find t for 400%2B%2850%29%2Aln%2890t%2B1%29=%285%2F100%29%2812300%2B1000ln%28t%2B1%29%29.
Do the necessary algebra steps to solve for t.