Question

if $4000 is invested at 5% simple interest, the initial value and the future value s at the end of each of 5 years is shown in the table below. then answer part (a) through (d).

year (t)	0	1	2	3	4	5

the future value of this investment at the end of the tth year is $5400.
is this an interpolation or an extrapolation from the data?
a. interpolation
b. extrapolation
(d) should this model be interpreted discretely or continuously?
a. continuously, because the simple interest is calculated continuously
b. discretely, because the simple interest is calculated yearly

Explanation:

Part (about interpolation/extrapolation):

Interpolation is estimating within known data (years 0 - 5 here), extrapolation is beyond (e.g., year \( t \) where \( S = 5400 \) is beyond year 5's \( 5000 \)). So it's extrapolation.

Simple interest here is calculated yearly (data is at year 0,1,2,...), so the model is discrete (values at distinct, separate time points: years).

Answer:

B. Extrapolation

Part (d):