Which statement describes the relationship between the function and its inverse?
1 answer:
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1) 155.91 grams would be left after 10 years
2) The population would be 376,478 in 2040
Step-by-step explanation:
The form of the exponential function is , where
- a is the initial amount (y at x = 0)
- b is the growth/decay factor
- b = 1 + r, where r is the rate of growth
- b = 1 - r, where r is the rate of decay
1)
Scientists are studying a 500 grams sample of a radioactive element, which has an annual decay rate of 11%
∵ The initial amount is 500 grams
∴ a = 500
∵ The annual decay rate is 11%
∴ r = 11% = 11 ÷ 100 = 0.11
∵ b = 1 - r ⇒ decay
∴ b = 1 - 0.11 = 0.89
- We need to find how many grams of the sample would be left
after 10 years
∴ x = 10
- Substitute all of these values in the form of the exponential function
∵
∴ y = 155.9085996
- Round it to 2 decimal places
∴ y = 155.91
155.91 grams would be left after 10 years
2)
In 2000, the population of an Ohio town was 140,212. The population is expected to grow at a rate of 2.5% each year
∵ The population of an Ohio town was 140,212
∴ a = 140.212
∵ The population is expected to grow at a rate of 2.5% each year
∴ r = 2.5% = 2.5 ÷ 100 = 0.025
∵ b = 1 + r ⇒ growth
∴ b = 1 + 0.025 = 1.025
- We need to find the population in 2040
∵ The number of years is 2040 - 2000 = 40 years
∴ x = 40
- Substitute all of these values in the form of the exponential function
∵
∴ y = 376478.1709
- Round it to the nearest whole number
∴ y = 376,478
The population would be 376,478 in 2040
Learn more:
You can learn more about the functions in brainly.com/question/11921476
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