Using an exponential function, it is found that:
- For Country A, the doubling time is of 43 years.
- For Country B, the growth rate is of 1.9% per year.
<h3>What is the exponential function for population growth?</h3>
The exponential function for population growth is given as follows:
In which:
- P(t) is the population after t years.
- P(0) is the initial population.
- k is the exponential growth rate, as a decimal.
For Country A, we have that k = 0.016. The doubling time is t for which P(t) = 2P(0), hence:
t = 43 years.
For Country B, P(36) = 2P(0), hence we have to solve for k to find the growth rate.
k = 0.019.
For Country B, the growth rate is of 1.9% per year.
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Based on the number of songs in each genre that Josiah listened to, the statements about his solution that are true are:
- He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.
- He did not multiply the numerator and denominator by the correct number to equal 1,500.
- He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
<h3>What did Josiah do wrong?</h3>
To find the average of the number of rock songs, he should have taken the average of rock songs he listened to which were 4 and 6:
= (4 + 6) / 2
= 5
Because he has a total of 1,500 songs on his player, he should have multiplied both the numerator and denominator by a number that would lead to 1,500 which is 75 and not 30.
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Answer:
The domain of g(x) is the same as the domain of the parent function.
The range is the same as the range of the parent function.
The function g(x) increases over the same x-values as the parent function.
The function g(x) decreases over the same x-values as the parent function.
