Looking at the image, I can see it’s a worksheet titled “Algebra Skill Builder: Exponential Growth and Simple Interest Problems.” It contains three word problems related to exponential growth (compound interest) and simple interest.
Since the user did not select any of the options (ExplainAnswer, TeachTopic, GeneratePractice are all false), I will solve the problems directly and provide only the final answers as instructed.
Let me solve each problem step by step:
---
Problem 1:
> You invest $5000 in a savings account which pays 3% interest compounded annually. What will the value of the money be after 10 years?
Formula for compound interest:
A = P(1 + r)^t
Where:
P = principal = $5000
r = annual interest rate = 3% = 0.03
t = time in years = 10
A = 5000 × (1 + 0.03)^10
A = 5000 × (1.03)^10
Calculate (1.03)^10 ≈ 1.343916
A ≈ 5000 × 1.343916 ≈ 6719.58
✔ Final Answer for Problem 1:
$6719.58
---
Problem 2:
> You invest $3000 in a savings account which pays 2.5% interest compounded quarterly. What will the value of the money be after 5 years?
Formula for compound interest with quarterly compounding:
A = P(1 + r/n)^(nt)
Where:
P = $3000
r = 2.5% = 0.025
n = 4 (quarterly)
t = 5 years
A = 3000 × (1 + 0.025/4)^(4×5)
A = 3000 × (1 + 0.00625)^20
A = 3000 × (1.00625)^20
Calculate (1.00625)^20 ≈ 1.132708
A ≈ 3000 × 1.132708 ≈ 3398.12
✔ Final Answer for Problem 2:
$3398.12
---
Problem 3:
> A property is initially valued at $150,000 but loses 2% of its value every year. What will the value of the property be after 10 years?
This is exponential decay:
A = P(1 - r)^t
Where:
P = $150,000
r = 2% = 0.02
t = 10 years
A = 150000 × (1 - 0.02)^10
A = 150000 × (0.98)^10
Calculate (0.98)^10 ≈ 0.817073
A ≈ 150000 × 0.817073 ≈ 122560.95
✔ Final Answer for Problem 3:
$122,560.95
---
Final Answer:
Problem 1: $6719.58
Problem 2: $3398.12
Problem 3: $122,560.95
Parent Tip: Review the logic above to help your child master the concept of exponential growth and decay word problems worksheet answer key.
