The population of a small town
decreases by one-tenth every year. Today, the population is 5000. Write an expression for the
population in 𝑡 years. Hint: by what do you multiply to
produce a decrease of one-tenth?
Let’s first convert one-tenth into a
percentage or one-tenth is equal to 10 percent. This means that we have a 10
percent decrease. As the population is decreasing by
10 percent each year, the new population will be 90 percent of the previous
year. 100 minus 10 equals 90. This means that our multiplier will
be 0.9 as 90 percent is the same as 0.9.
After one year, the population
would be 5000 multiplied by 0.9. After two years, the new population
would be 5000 multiplied by 0.9 squared. This means that after 𝑡 years, an
expression for the population would be 5000 multiplied by 0.9 to the power of
𝑡. This expression could be used to
calculate the population at any time in the future assuming that it continues to
decrease by one-tenth every year.