Question

1. rentals in a high - rise apartment building get more expensive the higher up, since the views get better. the ground floor (floor 0) rent is $1,220. the rent increases 2% per floor. what is the rent on the 8th floor?

circle: growth / decay
equation:
p = r = t =
rent on the 8th floor:

Explanation:

Step1: Identify the type of problem

This is an exponential growth problem. The formula for exponential growth is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the growth rate (as a decimal), and $t$ is the time (or in this case, the number of floors).

Step2: Determine the values of P, r, and t

• $P$ (initial rent on floor 0) is $\$1220$.
• $r$ (growth rate per floor) is $2\%$ or $0.02$ (since $2\%=\frac{2}{100}=0.02$).
• $t$ (number of floors we are moving up, from floor 0 to floor 8) is $8$.

Step3: Plug the values into the formula

Using the formula $A = P(1 + r)^t$, we substitute $P = 1220$, $r = 0.02$, and $t = 8$:
$$A = 1220(1 + 0.02)^8$$
First, calculate $(1 + 0.02) = 1.02$. Then, calculate $1.02^8$. Let's compute $1.02^8$:
$1.02^1 = 1.02$
$1.02^2 = 1.02\times1.02 = 1.0404$
$1.02^3 = 1.0404\times1.02 = 1.061208$
$1.02^4 = 1.061208\times1.02 = 1.08243216$
$1.02^5 = 1.08243216\times1.02 = 1.104080803$
$1.02^6 = 1.104080803\times1.02 = 1.126162419$
$1.02^7 = 1.126162419\times1.02 = 1.148685667$
$1.02^8 = 1.148685667\times1.02 \approx 1.17165938$

Now, multiply this by $1220$:
$A = 1220\times1.17165938 \approx 1220\times1.1717 \approx 1429.47$ (rounded to the nearest cent)

Step4: Fill in the values for P, r, t, and the equation

• Circle: Growth (since the rent is increasing)
• Equation: $A = 1220(1 + 0.02)^t$
• $P = 1220$, $r = 0.02$, $t = 8$
• Rent on the 8th floor: $\approx \$1429.47$

Answer:

• Circle: Growth
• Equation: $A = 1220(1 + 0.02)^t$
• $P = 1220$, $r = 0.02$, $t = 8$
• Rent on the 8th floor: $\approx \$1429.47$ (or more precisely, if we use a calculator for $1.02^8$: $1.02^8 = e^{8\ln(1.02)} \approx e^{8\times0.0198026} \approx e^{0.158421} \approx 1.171659$, so $1220\times1.171659 \approx 1429.42$)