Let’s solve each circled problem one by one. We’ll look at the equation, figure out if it’s growth or decay, find the initial value, and then find the rate.
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Problem 2: y = 55 · (1 - 0.02)^t
Step 1: Look at the part inside the parentheses: (1 - 0.02).
Since we’re subtracting from 1, this means the amount is getting smaller over time →
exponential decay.
Step 2: The number in front (55) is the starting amount →
initial value = 55.
Step 3: The rate is the number being subtracted: 0.02. To write as a percent, multiply by 100 →
rate of decay = 2%.
✔ Final for #2: Decay, Initial = 55, Rate = 2%
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Problem 4: y = 5575 · (0.65)^t
Step 1: The base is 0.65. Since 0.65 < 1, the function gets smaller over time →
exponential decay.
Step 2: The number in front is 5575 →
initial value = 5575.
Step 3: For decay, the rate is how much is lost each time.
We can think: 1 - 0.65 = 0.35 → so 35% is lost each time →
rate of decay = 35%.
✔ Final for #4: Decay, Initial = 5575, Rate = 35%
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Problem 6: y = 14000 · (0.92)^t
Step 1: Base is 0.92. Since 0.92 < 1, it’s decreasing →
exponential decay.
Step 2: Number in front is 14000 →
initial value = 14000.
Step 3: Rate of decay = 1 - 0.92 = 0.08 → convert to percent: 0.08 × 100 = 8% →
rate of decay = 8%.
✔ Final for #6: Decay, Initial = 14000, Rate = 8%
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Final Answer:
Problem 2: Exponential decay; initial value = 55; rate of decay = 2%
Problem 4: Exponential decay; initial value = 5575; rate of decay = 35%
Problem 6: Exponential decay; initial value = 14000; rate of decay = 8%
Parent Tip: Review the logic above to help your child master the concept of exponential growth and decay worksheet answers.
