Special Equations (Growth Formula) Casio fx-9750GII

Question

In the year 200, the number of text messages sent in a small town was 120. If the number of text messages grew every year afterward by 124%, how many years would it take for the number of text messages to surpass 36,000?

Formula: y=a(1+r)^t

36,000= 120(2.24)^t

^{-------------------------------}

¹²⁰

^120=(2.24)t

log_2.24300 = log_2.24(log 2.24)^t

^7.07=t

So I solved the problem, but that is not my question as I can clearly see that 2.24^7.07= 2.99.4011676.

My question is how do I calculate this on Casio fx-9750GII?

And also, is there a way to solve this problem without a calculator (even better!)?

Answer 1

I can't help you with the Casio directly, but I can help.

Your initial equation is correct.

Then you need to write is as

log 36000=log 120 + t log 2.24

then t = (log 36000-log 120)/log 2.24

You should be able to get common (Briggs or base 10) logarithms on your calculator and do the division.

If you can't get common logs on your calculator, you should be able to find a table of common logarithms somewhere (engineering book, math book, or somewhere online though I've never looked).

In fact, let me just give you the numbers you need

log 36000=4.556303

log 120=2.079181

log 2.24=.350248

Have at it!