-0.002x dx . 8. The proportion of light bulbs which last longer thant hours is given by | 0.002 e Find the proportion of light bulbs lasting more than t = 1200 hours. Express your answer in decimal, rounded to 4 decimal places. Show all reasoning in detail

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Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
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-0.002.x
8. The proportion of light bulbs which last longer than t hours is given by | 0.002 e
'dx.
Find the proportion of light bulbs lasting more than t = 1200 hours. Express your answer in decimal, rounded
to 4 decimal places. Show all reasoning in detail
9 Your hot cocoa (initially at a temperature of 190 °F) will cool at a rate which is proportional to the
difference between your cocoa's current temperature (“y") and ambient room temperature (65 °F ). Suppose
that the temperature (y) of your hot cocoa satisfies the differential equation
dy
2.5(y – 65) °F/hour, where t is the number of hours since your cocoa was brought into
dt
the 65 °F room. Solve this separable differential equation and initial condition (y(0) = 190 °F) to find a
formula for the temperature of your cocoa as a function of time. Your final answer should be in the form, y = a
function of t. Show all work in detai
Transcribed Image Text:-0.002.x 8. The proportion of light bulbs which last longer than t hours is given by | 0.002 e 'dx. Find the proportion of light bulbs lasting more than t = 1200 hours. Express your answer in decimal, rounded to 4 decimal places. Show all reasoning in detail 9 Your hot cocoa (initially at a temperature of 190 °F) will cool at a rate which is proportional to the difference between your cocoa's current temperature (“y") and ambient room temperature (65 °F ). Suppose that the temperature (y) of your hot cocoa satisfies the differential equation dy 2.5(y – 65) °F/hour, where t is the number of hours since your cocoa was brought into dt the 65 °F room. Solve this separable differential equation and initial condition (y(0) = 190 °F) to find a formula for the temperature of your cocoa as a function of time. Your final answer should be in the form, y = a function of t. Show all work in detai
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