Borrowing money: Suppose that you borrow $10,000 at 7%APR and that interest is compounded continuously. The equation of change for your account balance B = B(t) is Here t is the number of years since...

Borrowing money: Suppose that you borrow $10,000 at 7%APR and that interest is compounded continuously. The equation of change for your account balance B = B(t) is

Here t is the number of years since the account was opened, and B is measured in dollars.

a. Explain why B is an exponential function.

b. Find a formula for B using the alternative form for exponential functions.

c. Find a formula for B using the standard form for exponential functions. (Round the growth factor to three decimal places.)

d. Assuming that no payments are made, use your formula from part b to determine how long it would take for your account balance to double.