Total Change Theorem During a 40-minute workout, a person riding an exercise machine burns calories at a rate of c calories per minute, where the function y = c(t) is given in the figure to the left. On the interval 0

Total Change Theorem During a 40-minute workout, a person riding an exercise machine burns calories at a rate of c calories per minute, where the function y = c(t) is given in the figure to the left. On the interval 0

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter10: Radical Functions And Equations

Section10.1: Graphing Square Root Functions

Problem 46E

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Total Change Theorem
During a 40-minute workout, a person riding an exercise
machine burns calories at a rate of c calories per minute,
30
where the function y = c(t) is given in the figure to the
left. On the interval 0 <t< 10, the formula for c is
25
c(t) = -0.05t2 +t+ 10, while on 30 <t< 40, its
20
formula is c(t) = -0.05t2 + 3t – 30.
15
Which part of the expression do you need to use to find
the total calories between from t= 10 to t = 30?
10
5
O c(t) = -0.05?
+t+ 10
20
30
O c(t) = -0.05t2 + 3t + -30
40
min
10
-5
O neither of those parts
-10
That's right! For this part, we will need to look at the
behavior of c(t) on the graph to determine our integral.
-15
What is the exact total number of calories they burn from
t = 10 to t= 30? Show your work in the box below:
The total amount burned in from t= 10 to t= 30 is
cal/min

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