A population numbers 12,000 organisms initially and decreases by 2% each year.

Question

A population numbers 12,000 organisms initially and decreases by 2% each year.

Suppose PP represents population, and tt the number of years of growth. Write an exponential model to represent this situation.

Answer 1

P=12000(b)^t (when t = 0 the initial population is 12000).

Now, how to find b?

When you are given a percentage decrease subtract that value from 100% to get the percentage of organisms remaining: 100 - 2= 98%. Then convert to decimal. So b = .98.

Note that 12000(.98)^t = 12000(.98) when t = 1. After 1 year there are 11760 organisms.

When t = 2, this is the calculation that is being performed: (12000 (.98) (.98), So after 2 years there is 98% of the 11760 organisms that were there after 1 year.

P = 12000(.98)^t (that is the exponential model modeling this situation).

Note that if the population was increasing by 2% each year, then b = 100% + 2 % converted to decimal, i.e. 1.02).

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