In real world applications, measurements of certain quantities such as position, temperature, number of individuals, and...
In real world applications, measurements of certain quantities such as position, temperature, number of individuals, and concentrations are taken at specific points in time. The rate of change of these quantities can be estimated using the rise over run formula for slope. This may also be used to estimate the derivative of a function f that is not known.
Select Function 1,
T(t) = 50e−0.5t,
under the Explore & Test section of the Explore It.
(a) A scientist wants to know the temperature of a solution at 5
seconds. Set the t-coordinate of the fixed point to 5.
What is the temperature at 5 seconds to one decimal place?
°C
(b) The scientist wants to use the secant line to estimate the
cooling rate after 5 seconds. Drag the adjustable point to time 6.
What is the rise over run of the secant line? (Round your answer to
one decimal place.)
°C/min
(c) Now drag the adjustable point to time 5.5. What is the rise
over run? (Round your answer to one decimal place.)
°C/min
(d) What is the slope of the secant line in part (c) to one decimal
place?
°C/min
(e) Continue to move the adjustable point toward the fixed point
until the secant and tangent lines overlap. What is the slope of
the tangent line to one decimal place (the instantaneous cooling
rate)?
°C/min
Homework Answers
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Thank you
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