SOLUTION: The amount of land in the US farms may be modeled by F(t)= 115.1(0.9352)^t + 900 million acres. According to the model in what year will the amount of land in the US drop bellow 9

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Question 241422: The amount of land in the US farms may be modeled by F(t)= 115.1(0.9352)^t + 900 million acres. According to the model in what year will the amount of land in the US drop bellow 910 million acres. Could i please get help do not understand how to solve this problem.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There isn't enough information to know what
year it's starting at.
I'm assuming that t is the number of years
that have passed, and t+=+0 is the 1st year
F%28t%29+=+115.1%2A.9352%5Et+%2B+900
F%280%29+=+115.1%2A.9352%5E0+%2B+900
F%280%29+=+115.1%2A1+%2B+900
F%280%29+=+1015.1 million acres the 1st year
When does the land total 910 million acres?
F%28t%29+=+910
910+=+115.1%2A.9352%5Et+%2B+900
Subtract 900 from both sides
10+=+115.1%2A.9352%5Et
Take the log to the base 10 of both sides, noting that
log%2810%29+=+1
log%28a%2Ab%29+=+log%28a%29+%2B+log%28b%29
log%28a%5Eb%29+=+b%2Alog%28a%29
1+=+log%28115.1%29+%2B+t%2Alog%28.9352%29
1+=+2.061+-+.0291t
.0291t+=+2.061+-+1
.0291t+=+1.061
t+=+36.46
and
.46%2A12+=+5.52
t is about equal to 36 years and 5 months.
Sometime in the 5th month of the 36th year,
the farm acres drops below 910