A function is given
r(t) - 5 - ; t = 5,t = 10
(a) Determine the net change between the given values of the variable.
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Answered by
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Step-by-step explanation:
Answer and Explanation:
a. Given:
f(t)=4t2t1=2t2=2+h
f
(
t
)
=
4
t
2
t
1
=
2
t
2
=
2
+
h
Let's identify the net change between the independent variable t values:
Δt=t2−t1=2+h−2=h
Additionally, the change in function values (or the dependent variable values) is equivalent to:
f(t2)−f(t1)=4t
2
2
−4t
2
1
=4(t
2
2
−t
2
1
)=4(t2−t1)(t2+t1)=4(2+h−2)(2+h+2)=4h(4+h)
b. Using the average rate of change formula:
ravg=
f(t2)−f(t1)
t2−t1
=
f(t2)−f(t1)
Δt
=
4t
2
2
−4t
2
1
t2−t1
=4
(t2−t1)(t2+t1)
t2−t1
=4(t2+t1)=4⋅(2+2+h)=4⋅(4+h)=16+4h
Therefore, the net change between the t values is Δt=h and the average rate of change is ravg=16+4h
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