(Assume continuous compounding. Round your answer to the nearest cent.) $ If the average cost of a textbook in 2012 was $140, what is the actual inflation rate (rounded to the nearest tenth percent)? %
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Inflation and Textbook Cost Projections
In 1982 the inflation rate hit 16%. Suppose that the average cost of a textbook in 1982 was $20. What was the expected cost in the year 2017 if we project this rate of inflation on the cost? (Assume continuous compounding. Round your answer to the nearest cent.)
**Expected Cost in 2017:**
$ [____]
If the average cost of a textbook in 2012 was $140, what is the actual inflation rate (rounded to the nearest tenth percent)?
**Actual Inflation Rate:**
[____] %
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### Instructions:
1. **Continuous Compounding Formula:** To solve for the expected cost in 2017 using continuous compounding, utilize the formula:
\[ A = P \cdot e^{rt} \]
where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (initial cost in 1982).
- \( r \) is the annual interest rate (inflation rate).
- \( t \) is the time the money is invested or borrowed for, in years.
- \( e \) is the base of the natural logarithm, approximately equal to 2.71828.
2. **Practical Steps:**
- Calculate the time difference between 1982 and 2017 to get \( t \).
- Substitute \( P = 20 \), \( r = 0.16 \), and \( t = \) (number of years from 1982 to 2017) into the formula to find \( A \).
- Round your answer to the nearest cent.
3. **Actual Inflation Rate for 2012:** To find the actual inflation rate, use the given costs and the time span. The formula for continuous compounding will be rearranged to solve for \( r \), the actual inflation rate.
### Example Calculation:
- Time difference (\( t \)): 2017 - 1982 = 35 years
- Initial Cost (\( P \)): $20
- Annual Inflation Rate (\( r \)): 16% or 0.16
\[ A = 20 \times e^{0.16 \times 35} \]
By solving this, you should get the expected cost in 2017.
For the actual inflation rate:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F373e3400-461c-4f07-afaf-9f92fd60170d%2Fa29f3ba7-4ab8-4471-913d-5ceebdeea2ce%2Fbnoh1b_processed.png&w=3840&q=75)
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