Question 277891
your formula should read:


A = 1236 * (.97)^T where:


A is the future population.
T is the time in years.



The ^ indicates exponentiation.


According to the equation model, the initial population is 1236.


The general form of the equation is:


F = P * (1+G)^T where:


F = the future population
P = the present population
G = the annual growth rate
T = the number of years


In your equation:

F = A
P = 1236
G = -.03 because 1 - .03 = .97
T = number of years


Your equation becomes:


A = 1236 * .97^T


Since A is the future population, then A becomes 846.


Your equation becomes:


846 = 1236 * .97^T


Divide both sides of this equation by 1236 to get:


846/1236 = .97^T


Take the log of both sides of this equation to get:


log(846/1236) = log(.97^T)


Since log(a^b) = b*log(a), your equation becomes:


log(846/1236) = T*log(.97)


Divide both sides of this equation by log(.97) to get:


log(846/1236)/log(.97) = T which is the same as:


T = log(846/1236)/log(.97)


use your calculator to find the logs which make your equation equal to:


T = -.164648108 / -.013228266 = 12.44668886


The future population will be 846 in 12.4466886 years.


1236 * .97^(12.44668886) = 846


Round that to the nearest hundredth of a year and you get:


T = 12.45