1.

A function is givenr(t) - 5 - ; t = 5,t = 10(a) Determine the net change between the given values of the variable.​

Answer»

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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