Question

Carmen deposits $4000 into a simple interest account. The interest rate for the account is 4.25%.

Write a function that represents the balance in the account as a function of time t.

Answer 1

Answer: f(t) = 170t+4000

t = number of years

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Step-by-step explanation:

We use the simple interest formula which is

i = P*r*t

where in this case,

• P = 4000 = amount deposited aka principal
• r = 0.0425 = decimal form of the 4.25% annual interest rate
• t = unknown number of years

We then get the following

i = P*r*t

i = 4000*0.0425*t

i = 170t

Showing that the amount of simple interest earned is 170 times that of the number of years.

For instance, if Carmen waits t = 10 years, then she earns i = 170*t = 170*10 = 1700 dollars in interest alone.

The expression 170t is the interest only. Add on the original amount deposited to find the total account balance after t years. Therefore, we arrive at 170t+4000 to get the linear function f(t) = 170t+4000

The 170 acts like the slope while the 4000 is the y intercept.

Answer 2

answer : f(t) = 4000 + 170t

f(t) = principal + (principal multiplied by interest rate) multiplied by time

f(t) = 4000 + (4000*.0425)t

f(t) = 4000 + 170t