Here are the step-by-step solutions for each problem on the worksheet.
1. Bacteria Growth
*
Identify the values: Start amount ($P$) = 800, Rate ($r$) = 9% (or 0.09), Time ($t$) = 5 hours.
*
Formula: $A = P(1 + r)^t$
*
Calculation:
* $A = 800(1 + 0.09)^5$
* $A = 800(1.09)^5$
* $1.09^5 \approx 1.53862$
* $800 \times 1.53862 \approx 1230.9$
* Since we can't have a fraction of a bacterium, we round to the nearest whole number.
2. Truck Depreciation
*
Identify the values: Start value ($P$) = \$32,000, Rate ($r$) = -5% (or -0.05 because it is losing value), Time ($t$) = 5 years.
*
Formula: $A = P(1 - r)^t$
*
Calculation:
* $A = 32,000(1 - 0.05)^5$
* $A = 32,000(0.95)^5$
* $0.95^5 \approx 0.77378$
* $32,000 \times 0.77378 \approx 24,761.00$
3. Lottery CD Investment
*
Identify the values: Start amount ($P$) = \$15,000, Rate ($r$) = 4% (or 0.04), Time ($t$) = 4 years.
*
Formula: $A = P(1 + r)^t$
*
Calculation:
* $A = 15,000(1 + 0.04)^4$
* $A = 15,000(1.04)^4$
* $1.04^4 \approx 1.16986$
* $15,000 \times 1.16986 \approx 17,547.87$
4. Boat Depreciation
*
Identify the values: Start value ($P$) = \$25,000, Rate ($r$) = 18% (or 0.18), Time ($t$) = 3 years.
*
Formula: $A = P(1 - r)^t$
*
Calculation:
* $A = 25,000(1 - 0.18)^3$
* $A = 25,000(0.82)^3$
* $0.82^3 = 0.551368$
* $25,000 \times 0.551368 = 13,784.20$
5. Cancer Cell Growth
*
Identify the values: Start amount ($P$) = 10,000, Rate ($r$) = 22% (or 0.22), Time ($t$) = 4 days.
*
Formula: $A = P(1 + r)^t$
*
Calculation:
* $A = 10,000(1 + 0.22)^4$
* $A = 10,000(1.22)^4$
* $1.22^4 \approx 2.21533$
* $10,000 \times 2.21533 \approx 22,153.35$
* Rounding to the nearest whole cell gives 22,153.
6. Bacteria Doubling
*
Identify the values: Start amount ($P$) = 1, Rate = Doubles (multiplier is 2), Time ($t$) = 30 days.
*
Formula: $A = P(2)^t$
*
Calculation:
* $A = 1(2)^{30}$
* $2^{30} = 1,073,741,824$
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Final Answer:
1. Approximately 1,231 bacteria
2. $24,761.00
3. $17,547.87
4. $13,784.20
5. Approximately 22,153 cells
6. 1,073,741,824 bacteria
Parent Tip: Review the logic above to help your child master the concept of exponential growth and decay word problems worksheet answer key.
