a quantity with an initial value of 830 grows exponentially at a rate s…
2347.57
Question
a quantity with an initial value of 830 grows exponentially at a rate such that the quantity doubles every 2 weeks. what is the value of the quantity after 21 days, to the nearest hundredth?
Solution Steps
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Understand the question
a quantity with an initial value of 830 grows exponentially at a rate such that the quantity doubles every 2 weeks. what is the value of the quantity after 21 days, to the nearest hundredth?
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Explanation
Step1: Convert time to consistent units
21 days = $\frac{21}{7}$ = 3 weeks
Step2: Define exponential growth formula
The formula for exponential growth with doubling time is $A = A_0 \times 2^{\frac{t}{d}}$, where $A_0$ is initial value, $t$ is time elapsed, $d$ is doubling time.
Here, $A_0 = 830$, $t=3$, $d=2$.Step3: Substitute values into formula
$A = 830 \times 2^{\frac{3}{2}}$
Step4: Calculate the exponent and result
$2^{\frac{3}{2}} = 2\sqrt{2} \approx 2.8284$
$A \approx 830 \times 2.8284$
$A \approx 2347.572$Step5: Round to nearest hundredth
Round 2347.572 to two decimal places.
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Final answer
2347.57
Answer
Explanation
Step1: Convert time to consistent units
21 days = $\frac{21}{7}$ = 3 weeks
Step2: Define exponential growth formula
The formula for exponential growth with doubling time is $A = A_0 \times 2^{\frac{t}{d}}$, where $A_0$ is initial value, $t$ is time elapsed, $d$ is doubling time.
Here, $A_0 = 830$, $t=3$, $d=2$.
Step3: Substitute values into formula
$A = 830 \times 2^{\frac{3}{2}}$
Step4: Calculate the exponent and result
$2^{\frac{3}{2}} = 2\sqrt{2} \approx 2.8284$
$A \approx 830 \times 2.8284$
$A \approx 2347.572$
Step5: Round to nearest hundredth
Round 2347.572 to two decimal places.
Answer
2347.57
Question Image
Click to enlargeQuestion Analysis
Subject
mathematics
Sub Subject
calculus
Education Level
high school
Difficulty
unspecified
Question Type
calculation
Multi Question
No
Question Count
1
Analysis Status
completed
Analyzed At
2026-02-09T20:32:06
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a quantity with an initial value of 830 grows exponentially at a rate such that the quantity doubles every 2 weeks. what is the value of the quantity after 21 days, to the nearest hundredth?
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