Recently I have been working with applying exponential equations to the real world. However, one question completely threw me as is laid out below:
Q. The population of a town, N, is modeled by the function N = 15000(2 ^ 0.01t), where "t" is the number of years since 1980. In what year will the population reach 20000 people?
A. Okay, well to start off with, the general form of an exponential equation is:
y = ab ^ x
I know that "a" is the initial value and in this case is 15000.
N = 15000(2 ^ 0.01t)
I substitute N for 20000
20000 = 15000(2 ^ 0.01t)
Then do I divide both sides by 15000? And Once I have done that, and have transformed the equation into logarithmic form, how do I solve for "t"? Normally, it's quite easy, but in this case, the power of "t" is prefixed with "0.01", and I am unsure how to work with that.
Any help on solving this will be much appreciated!