Question

problem 3
clare made $160 babysitting last summer. she put the money in a savings account that pays 3% interest per year. if clare doesnt touch the money in her account, she can find the amount shell have the next year by multiplying her current amount by 1.03.
a. how much money will clare have in her account after 1 year? after 2 years?
b. how much money will clare have in her account after 5 years? explain your reasoning.
c. write an expression for the amount of money clare would have after 30 years if she never withdraws money from the account.
problem 4
the equation $y = 5,280x$ gives the number of feet, $y$, in $x$ miles. what does the number 5,280 represent in this relationship?

Explanation:

Problem 3

Step1: Calculate amount after 1 year

Multiply principal by 1.03.
$\$160 \times 1.03 = \$164.80$

Step2: Calculate amount after 2 years

Multiply year 1 amount by 1.03.
$\$164.80 \times 1.03 = \$169.74$

Step3: Calculate amount after 5 years

Use compound interest formula $A = P(1+r)^t$, where $P=160$, $r=0.03$, $t=5$.
$\$160 \times (1.03)^5 \approx \$160 \times 1.159274 = \$185.48$

Step4: Write 30-year amount expression

Apply compound interest formula for $t=30$.
$160 \times (1.03)^{30}$

The equation $y = 5280x$ converts miles to feet. In a linear relationship $y = kx$, $k$ is the conversion factor between the two units.

Answer:

a. After 1 year: $\$164.80$; After 2 years: $\$169.74$
b. $\$185.48$ (This uses annual compound interest, where each year's balance is 1.03 times the previous year's, so we calculate the principal multiplied by $1.03$ raised to the 5th power.)
c. $160(1.03)^{30}$

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Problem 4