a quantity with an initial value of 160 grows continuously at a rate of…
167.12
Question
a quantity with an initial value of 160 grows continuously at a rate of 0.65% per hour. what is the value of the quantity after 402 minutes, to the nearest hundredth?
Solution Steps
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Understand the question
a quantity with an initial value of 160 grows continuously at a rate of 0.65% per hour. what is the value of the quantity after 402 minutes, to the nearest hundredth?
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Explanation
Step1: Convert time to hours
$402 \text{ minutes} = \frac{402}{60} = 6.7 \text{ hours}$
Step2: Define continuous growth formula
The continuous growth formula is $A = Pe^{rt}$, where $P=160$, $r=0.0065$, $t=6.7$.
Step3: Calculate exponent term
$rt = 0.0065 \times 6.7 = 0.04355$
Step4: Compute exponential value
$e^{0.04355} \approx 1.04451$
Step5: Find final quantity
$A = 160 \times 1.04451$
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Final answer
167.12
Answer
Explanation
Step1: Convert time to hours
$402 \text{ minutes} = \frac{402}{60} = 6.7 \text{ hours}$
Step2: Define continuous growth formula
The continuous growth formula is $A = Pe^{rt}$, where $P=160$, $r=0.0065$, $t=6.7$.
Step3: Calculate exponent term
$rt = 0.0065 \times 6.7 = 0.04355$
Step4: Compute exponential value
$e^{0.04355} \approx 1.04451$
Step5: Find final quantity
$A = 160 \times 1.04451$
Answer
167.12
Question Image
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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
2026-02-09T20:30:22
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a quantity with an initial value of 160 grows continuously at a rate of 0.65% per hour. what is the value of the quantity after 402 minutes, to the nearest hundredth?
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