ast year, Heather opened an investment account with \( \$ 7500 \). At the end of the year, the amount in the account had increased by \( 7 \% \). (a) Fill in the blank to write the year-end amount in terms of the original amount. Write your answer as a decimal. Year-end amount \( =\square \times \) Original amount (b) Use your answer in part (a) to determine the year-end amount in Heather's account. Year-end amount: \( \$ \square \)

Let's solve each part step by step. ### (a) Year-End Amount in Terms of the Original Amount When an investment increases by a certain percentage, the year-end amount can be expressed by multiplying the original amount by **1 plus the percentage increase (as a decimal)**. - **Increase Percentage:** \( 7\% \) - **As a Decimal:** \( 0.07 \) So, the multiplier is: \[ 1 + 0.07 = 1.07 \] **Answer:** \[ \text{Year-end amount} = \boxed{1.07} \times \text{Original amount} \] ### (b) Calculating the Year-End Amount in Heather's Account Using the multiplier from part (a), we can calculate the year-end amount. - **Original Amount:** \( \$7,\!500 \) - **Multiplier:** \( 1.07 \) \[ \text{Year-end amount} = 1.07 \times \$7,\!500 \] \[ \text{Year-end amount} = \$7,\!500 + (\$7,\!500 \times 0.07) = \$7,\!500 + \$525 = \$8,\!025 \] **Answer:** \[ \text{Year-end amount}: \boxed{\$8,\!025} \]