Question
The function f, of, t, equals, 5400, left parenthesis, 1, point, 4, right parenthesis, start superscript, 24, t, end superscriptf(t)=5400(1.4)
24t
represents the change in a quantity over t days. What does the constant 1.4 reveal about the rate of change of the quantity?
Answer
Attempt 1 out of 2
The function is
exponentially at a rate of
% every
.
24t
represents the change in a quantity over t days. What does the constant 1.4 reveal about the rate of change of the quantity?
Answer
Attempt 1 out of 2
The function is
exponentially at a rate of
% every
.
Answers
Answered by
GPT-4o mini
The function \( f(t) = 5400 (1.4)^{24t} \) represents exponential growth, where \( 1.4 \) is the base of the exponential function.
To determine the rate of change, we can identify that \( 1.4 \) indicates that the quantity increases by a factor of \( 1.4 \) for every unit of time (in this case, every \( 24t \) days). This can also be expressed in terms of a percentage increase.
1. The growth factor per unit time is \( 1.4 \).
2. To find the growth rate as a percentage, we calculate:
\[
\text{Growth rate} = (1.4 - 1) \times 100\% = 0.4 \times 100\% = 40\%
\]
This means:
- The function is **growing exponentially** at a rate of **40%** every **24 days**.
Answer:
The function is growing exponentially at a rate of 40% every 24 days.
To determine the rate of change, we can identify that \( 1.4 \) indicates that the quantity increases by a factor of \( 1.4 \) for every unit of time (in this case, every \( 24t \) days). This can also be expressed in terms of a percentage increase.
1. The growth factor per unit time is \( 1.4 \).
2. To find the growth rate as a percentage, we calculate:
\[
\text{Growth rate} = (1.4 - 1) \times 100\% = 0.4 \times 100\% = 40\%
\]
This means:
- The function is **growing exponentially** at a rate of **40%** every **24 days**.
Answer:
The function is growing exponentially at a rate of 40% every 24 days.
There are no human answers yet. A form for humans to post answers is coming very soon!