Question 1130984


{{{P(t) = 5500(1.1)^t}}}, {{{0 <= t <= 8}}} where {{{t }}}is measured in years. 


(a)  the population at time 
{{{t = 0}}}

{{{P(0) = 5500(1.1)^0}}}

{{{P(0) = 5500(1)}}}

{{{P(0) = 5500}}}


and at time 

{{{t = 4}}}

{{{P(4) = 5500(1.1)^4}}}

{{{P(4) = 5500(1.4641)}}}

{{{P(4) = 8052.55}}}


so,
{{{P(0) = 5500}}}
{{{P(4) = 8052.55}}}


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


{{{11000= 5500(1.1)^t}}}


{{{11000/5500=(1.1)^t}}}


{{{110/55=(1.1)^t}}}

{{{(1.1)^t=2}}}..............take log of both sides


{{{log((1.1)^t)=log(2)}}}

{{{t*log((1.1))=log(2)}}}

{{{t=log(2)/log((1.1))}}}

{{{t=7.27254}}}.....round to the nearest whole number

{{{t=7}}}

the population will reach {{{11000}}} in  {{{7}}} yr