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You rent an apartment that costs
$1400 per month during the first year, but the rent is set to go up
10% per year. What would be the rent of the apartment during the 9th year of living in the apartment? Round your answer to the nearest whole number.
Answer:
$ □

You rent an apartment that costs $\$ 1400$ per month during the first year, but the rent is set to go up $10 \%$ per year. What would be the rent of the apartment during the $9$ th year of living in the apartment? Round your answer to the nearest whole number. $\newline$ Answer: $\$$ $\square$

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Exponential growth and decay: word problems

Full solution

Q. You rent an apartment that costs

\$ 1400

per month during the first year, but the rent is set to go up

10 \%

per year. What would be the rent of the apartment during the

9

th year of living in the apartment? Round your answer to the nearest whole number.

\newline

Answer:

\$

\square

Identify Rent Details: Identify the initial rent and the rate of increase. $\newline$ The initial rent is $\$1400$ per month, and the rent increases by $10\%$ each year.
Determine Rent Formula: Determine the formula for the rent after a certain number of years. $\newline$ The rent after $n$ years can be calculated using the formula for exponential growth: $P(n) = P_0 \times (1 + r)^n$ , where $P_0$ is the initial amount, $r$ is the rate of increase, and $n$ is the number of years.
Convert to Decimal: Convert the percentage increase to a decimal. $\newline$ A $10\%$ increase is the same as multiplying by $1.10$ (or adding $10\%$ of the initial amount to the initial amount each year).
Apply Formula for $9$ th Year: Apply the formula to find the rent for the $9$ th year. $P(9) = 1400 \times (1.10)^9$
Calculate Rent for $9$ th Year: Calculate the rent for the $9$ th year. $\newline$ $P(9) = 1400 \times (1.10)^9$ $\newline$ $P(9) = 1400 \times 2.35794769$ (rounded to $8$ decimal places) $\newline$ $P(9) = 3301.127166$ (rounded to $6$ decimal places)
Round to Nearest Whole Number: Round the answer to the nearest whole number. $\newline$ The rent for the $9$ th year, rounded to the nearest whole number, is $\$3301$ .

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