Write and Solve the Differential Equation That Models the Following $P$

question 85

Multiple Choice

Write and solve the differential equation that models the following verbal statement. Evaluate the solution at the specified value of the independent variable, rounding your answer to four Decimal places: The rate of change of $P$ is proportional to $P$ . When $t = 0 , P = 60$ and when $t = 5 , P = 84$ . What is the value of $P$ when $t = 11$ ?

• A) \(P ( 11 ) = 131.9962\)
• B) \(P ( 11 ) = 129.5362\)
• C) \(P ( 11 ) = 122.0362\)
• D) \(P ( 11 ) = 125.7862\)
• E) \(P ( 11 ) = 116.8662\)

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Definitions:

Periodic Interest Rate

The interest rate applied to a loan or investment for a specific period, shorter than a year, such as monthly or quarterly.

Annuity

An annuity is a financial offering that ensures a regular payout to an individual, chiefly employed as a means of financial support for retired persons.

Compounded Quarterly

Interest calculated and added to the principal every quarter (three months), which then accrues additional interest in subsequent quarters.

Economic Advantage

The benefit gained by making a decision that results in the optimal utilization of resources, leading to a better outcome compared to other alternative decisions.