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The population of a city increases by
5% per year. What should we multiply the current population by to find the next year's population in one step?
Answer:

The population of a city increases by $5 \%$ per year. What should we multiply the current population by to find the next year's population in one step? $\newline$ Answer:

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Exponential growth and decay: word problems

Full solution

Q. The population of a city increases by

5 \%

per year. What should we multiply the current population by to find the next year's population in one step?

\newline

Answer:

Understanding Percentage Increase: To find the factor by which we should multiply the current population to get the next year's population, we need to consider the percentage increase. A $5\%$ increase means that the new population is $100\%$ of the old population plus an additional $5\%$ . In terms of multiplication, this is the same as multiplying by $1$ (which represents the original $100\%$ ) plus $0.05$ (which represents the additional $5\%$ ).
Calculating Multiplication Factor: To express this as a single multiplication factor, we add $1$ (the original population) to $0.05$ (the increase), which gives us $1.05$ . This is the factor by which we multiply the current population to find the next year's population.

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