Question

The amount of money left on a loan that kira owes her grandmothers is represented by the function k(t)= 280(.88)^t where k(t) represents the amount of money left on the loan and t tepresents the time, in years.

1) Identify k(t) as growth or decay and explain your answer.

2) Name A0, startinf amount and explain what it represents.
3) Find r,the percent change and explain what it represents.
thank youso much!!!

Answer 1

The function k(t) = 280(.88)^t represents decay, A0 is the initial amount of the loan, and r is the percent change that represents the rate at which the loan decreases over time.

Step-by-step explanation:

1) Identify k(t) as growth or decay: The function k(t) = 280(.88)^t represents decay because the value of (.88)^t is less than 1, and as t increases, the value of k(t) decreases continuously.

2) Name A0, starting amount: A0 represents the initial amount or starting amount of the loan. In this case, A0 is the $280 that Kira initially owes to her grandmothers.

3) Find r, the percent change: The value of r can be found by taking the natural logarithm (ln) of (1 + p), where p is the growth rate. In this case, r = ln(0.88), which is approximately -0.1283. The percent change represented by r is the rate at which the loan decreases over time.

Answer 2

Given:
k(t) = 280 (.88)^t

t k(t)
0 280
1 246.40
2 216.83
3 190.81
4 167.91
5 147.76

k(t) is decay. The amount decreases as the number of years increases. This means that the loan is being paid off until it becomes 0.

280 is the starting amount. It is the amount loaned.

88% of the previous years amount is the remaining balance for the current year.