MHB Manipulating quadratic and exponential expressions

[mdp448]

I am having so much trouble figuring this out, I would really appreciate some help.

The question is:
The following function, L, gives the approximate percent literacy rate in India t years after 1900.

L(t)=5.3 x 1.025^t

Which of the following equivalent functions shows, as a constant or coefficient, the approximate number of years it took for the literacy rate to triple?

(a) L(t)=5.3 x 3^t/44.5
(b) L(t)=5.3 x 1.077^t/3
(c) L(t)=5.3 x 1.008^3t
(d) L(t)=3 x 1.025^t+23

Thanks so much. I know what the answer is, but I just have no idea why it is the answer. I just want to understand :(

 

[skeeter]

initial literacy percentage is $L(0) = 5.3 \cdot (1.025)^0 = 5.3$

triple literacy percentage is $3 \cdot 5.3$ ...

$3 \cdot 5.3 = 5.3 \cdot (1.025)^t$

$3 = 1.025^t$

$\log(3) = t\log(1.025) \implies t = \dfrac{\log(3)}{\log(1.025)} \approx 44.5 \text{ years}$

... now look at equation (a)