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Question

At the beginning of 2010 there were 1000 giraffes in a reserve. after T years the number of giraffes J is given by the expression 1000 (1.05)^t
After how many years (approximate to the whole) the reserve will have 1150 giraffes be held in the reserve?

ANSWERS:
A) 4
B)2
C)5
D)3
E)1

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Answer 1 · 2017-12-07T23:47:37

$t = 3$ $t=3$

We have equation:

$A (t) = 1000 {(1.05)}^{t}$ $A(t)=1000(1.05)^t$

1150 giraffes in reserve after t years, so:

$1150 = 1000 {(1.05)}^{t}$ $1150=1000(1.05)^t$

We solve for $t$ $t$ :

Divide both sides by 1000:

$\frac{1150}{1000} = {(1.05)}^{t}$ $1150/1000=(1.05)^t$

$1.15 = {(1.05)}^{t}$ $1.15=(1.05)^t$

Take logs of both sides:

$ln (1.15) = t ln (1.05)$ $ln(1.15)=tln(1.05)$

$\frac{ln (1.15)}{ln (1.05)} = t \Rightarrow t = 2.864551591$ $ln(1.15)/ln(1.05)=t=>t=2.864551591$

$t = 3$ $t= 3$ to nearest whole number.