Question

Elaine deposited $500 at 4.25% compounded continuously for t number of years. Model the given situation with a function showing the amount A, accumulated after t years.

Answer 1

The model for the accumulated amount A after t years with an initial deposit of $500 at 4.25% interest rate compounded continuously is A = $500e^{0.0425t}.

Step-by-step explanation:

The question involves finding a function that models the accumulated amount A, after t years when $500 is deposited at a 4.25% interest rate compounded continuously. To model this, we use the formula for continuous compounding:

A = Pe^(rt)

Where:

• P is the principal amount (the initial amount of money)
• r is the annual interest rate (in decimal form)
• e is the base of the natural logarithm (approximately 2.71828)
• t is the time in years

For Elaine's situation:

• P = $500
• r = 4.25% or 0.0425 in decimal form
• t = number of years

So the function modeling her account balance after t years is:

A = $500e0.0425t

This equation will calculate the future value received after t years when the initial deposit is compounded continuously at an interest rate of 4.25%.