SOLUTION: The population P of a city grows exponentially according to the function P(t) = 5500(1.1)^t, 0 ≤ t ≤ 8 where t is measured in years. (a) Find the population at t

Algebra ->  Inequalities -> SOLUTION: The population P of a city grows exponentially according to the function P(t) = 5500(1.1)^t, 0 ≤ t ≤ 8 where t is measured in years. (a) Find the population at t      Log On


   

Question 1130984: The population P of a city grows exponentially according to the function
P(t) = 5500(1.1)^t, 0 ≤ t ≤ 8
where t is measured in years.
(a) Find the population at time
t = 0
and at time
t = 4.
P(0) =
P(4) =
(b) When, to the nearest year, will the population reach 11,000? ________yr
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

P%28t%29+=+5500%281.1%29%5Et, 0+%3C=+t+%3C=+8 where t+is measured in years.

(a) the population at time
t+=+0
P%280%29+=+5500%281.1%29%5E0
P%280%29+=+5500%281%29
P%280%29+=+5500

and at time
t+=+4
P%284%29+=+5500%281.1%29%5E4
P%284%29+=+5500%281.4641%29
P%284%29+=+8052.55

so,
P%280%29+=+5500
P%284%29+=+8052.55

(b) When, to the nearest year, will the population reach 11000? ________yr

11000=+5500%281.1%29%5Et

11000%2F5500=%281.1%29%5Et

110%2F55=%281.1%29%5Et
%281.1%29%5Et=2..............take log of both sides

log%28%281.1%29%5Et%29=log%282%29
t%2Alog%28%281.1%29%29=log%282%29
t=log%282%29%2Flog%28%281.1%29%29
t=7.27254.....round to the nearest whole number
t=7
the population will reach 11000 in 7 yr