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The population of a city increases by
1.7% 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 $1.7 \%$ 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

1.7 \%

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

\newline

Answer:

Convert to Decimal: To find the multiplier that represents a $1.7\%$ increase, we need to express the percentage increase as a decimal and then add it to $1$ to get the total multiplier. $\newline$ $1.7\%$ as a decimal is $0.017$ .
Calculate Multiplier: Now, we add the decimal to $1$ to find the multiplier for the population increase. $\newline$ Multiplier = $1 + 0.017 = 1.017$
Check Calculation: We can check our calculation by considering a simple example. If the population were $100$ , a $1.7\%$ increase would add $1.7$ to it, resulting in a population of $101.7$ . This is the same as multiplying $100$ by $1.017$ .

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