Question

A hospital sends an invoice to a patient. The patient schedules a payment plan in which she makes an initial payment of $1,451 the first month and then pays one-third of the previous month’s payment each of the following months until the invoice is paid in full. Approximately how much of the invoice will be paid after the fourth month?

A. $1,451.00

B. $2,095.89

C. $2,149.63

D. $2,167.54

Answer 1

The correct option is C.

Explanation:

The exponential function is defined as

`f(x)=ab^x`

Where, a is the initial value and b is the growth factor.

The initial payment is 1451 and the payment of next month is one-third of the previous month’s.

The equation is

`f(x)=1451((1)/(3))^(x-1)`

where, x is number of months.

Amount of first month payments is

`f(1)=1451((1)/(3))^(1-1)=1451`

Amount of second month payments is

`f(2)=1451((1)/(3))^(2-1)=483.67`

Amount of third month payments is

`f(3)=1451((1)/(3))^(3-1)=161.22`

Amount of fourth month payments is

`f(3)=1451((1)/(3))^(4-1)=53.74`

The invoice will be paid after the fourth month

`1451+483.67+161.2+53.7=2149.63`

Therefore correct option is C.

Answer 2

1st payment = $1451
2nd payment = $1451 (1/3) = $483.67
3rd payment = $1452(1/3)² = $161.22
4th payment = $1451(1/3)³ = $53.74

Total after 4 payments = 1451 + 483.67 + 161.2 + 53.7 = $2149.63

Answer: C. $2,149.63