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Find common variables. I wrote the ones I found above the polynomial. write them in parentheses the first number will have the variable. now it's just a matter of figuring out how to order it so that the first terms added to the second terms equal to the middle term of the polynomial. ... I think this is right. you could always look on wikiHow if I'm wrong.
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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