Two thousand dollars is deposited into a savings account at 8.5% interest compounded continuously. (a) What is the formula for A(t), the balance after t years? (b) What differential equation is satisfied by A(t), the balance after t years? (c) How much money will be in the account after 5 years? (d) When will the balance reach $3000? (e) How fast is the balance growing when it reaches $3000?

a)

b)

c)$3059.1808

d)t=4.77 years

e) The balance growing is $254.99/year

Step-by-step explanation:

We are given that Two thousand dollars is deposited into a savings account at 8.5% interest compounded continuously.

Principal = $2000

Rate of interest = 8.5%

a) What is the formula for A(t), the balance after t years?

Formula

So,

B)What differential equation is satisfied by A(t), the balance after t years?

So,

c)How much money will be in the account after 5 years?

Substitute t = 5 in the formula "

d)When will the balance reach $3000?

Substitute A(t)=3000

So,

t=4.77

The balance reach $3000 in 4.77 years

e)How fast is the balance growing when it reaches $3000?

Substitute the value of t = 4.77 in derivative formula :

Hence the balance growing is $254.99/year