Question

Write the general antiderivative. (Use C for the constant of integration.)

t(x)=220(0.92) DVDs per week, x weeks since the end of June.
T(x)=
Identify the units of measure of the general antiderivative.
O weeks
O DVDs sold in June
weeks since the end of June
O DVDs per week
O DVDs

Answer 1

• Answer:

The General Antiderivative is:

T(x) = 220/2 ln(0.92)(0.92^x)^2 + C

The Units of Measure f the General Antiderivative are DVDs, Since it Represents the total Number of DVD's Sold after (x) Weeks Since the End of JUNE.

Explanation:

• Make a Plan:
• Integral Symbol: (∫ )

• Find the general Antiderivative of the given function:

t(x) = 220(0.92^x) and identify the units of measure.

• Solve the problem:

• 1 - Find the general Antiderivative of t(x)

T(x) = ∫ 220(0.92^x)dx

• 2 - Use Substitution Method:

Let: u = 0.92^x, then, du = 0.92^x ln(0.92)dx

• 3 - Rewrite the Integral:

T(x) ∫ 220/ln(0.92) udu

• 4 - Integrate with respect to u

T(x) = 220/ln(0.92) u^2/2 + C

• 5 - Substitute back (u) = 0.92^x:

T(x) = 220/2 ln (0.92) (0.92^x)^2 + C

• Draw the conclusion:

The General Antiderivative is:

T(x) = 220/2 ln(0.92)(0.92^x)^2 + C

The Units of Measure f the General Antiderivative are DVDs, Since it Represents the total Number of DVD's Sold after (x) Weeks Since the End of JUNE.

I hope this helps!