The mess in a house can be measured by M(t). Assume that at M(0) = 0, the house starts out clean. Over time the rate of change in the mess is proportional to (100 - M). After 5 hours the house has a mess index of 60. A completely messy house has a value of 100. How many hours does it take for the house to have a mess index of 95? O 8.25 O 12.35 O 16.37 O 25.47

College Algebra
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ISBN:9781938168383
Author:Jay Abramson
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Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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The mess in a house can be measured by M(t). Assume that at M(0) = 0, the house starts out clean. Over time the rate of change in
the mess is proportional to (100 - M). After 5 hours the house has a mess index of 60. A completely messy house has a value of 100.
How many hours does it take for the house to have a mess index of 95?
8.25
12.35
16.37
25.47
Transcribed Image Text:The mess in a house can be measured by M(t). Assume that at M(0) = 0, the house starts out clean. Over time the rate of change in the mess is proportional to (100 - M). After 5 hours the house has a mess index of 60. A completely messy house has a value of 100. How many hours does it take for the house to have a mess index of 95? 8.25 12.35 16.37 25.47
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