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1. When a certain object is placed in an oven at 540°C, its temperature T(t) rises according to the equation T(t) = 540(1 – e^–0.1t), where t is the elapsed time (in minutes).
What is the temperature after 10 minutes and how quickly is it rising at this time?
I have come to the conclusion that when plugging 10 into t I get 341.35 as the temperature, but I am unsure how to find out how quickly it is rising?
The amount of daylight a particular location on Earth receives on a given day of the year can be modelled by a sinusoidal function. The amount of daylight that Windsor, Ontario will experience in 2007 can be modelled by the function D(t) = 12.18 + 3.1 sin(0.017t – 1.376), where tis the number of days since the start of the year.
a) On January 1, how many hours of daylight does Windsor receive?
b) What would the slope of this curve represent?
c) The summer solstice is the day on which the maximum amount of daylight will occur. On what day of the year would this occur?
d) Verify this fact using the derivative.
e) What is the maximum amount of daylight Windsor receives?
f) What is the least amount of daylight Windsor receives?
I have found for a that it would be 9.15 hours of sun and that b would be the daily change in sunlight
, I am stuck with c through f :(
2. Homework Equations
T(t) = 540(1 – e^–0.1t)
D(t) = 12.18 + 3.1 sin(0.017t – 1.376),
The Attempt at a Solution
I have attempted some but the others unsure how to...[/B]