if $3000 is invested at 6% simple interest, the initial value and the future value s at the end of each of 5…

if $3000 is invested at 6% 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).\n|year (t)|0|1|2|3|4|5|\n|future value (s)|3000|3180|3360|3540|3720|3900|\n(a) s = 180t + 3000 (type an equation.)\n(b) a linear model cannot exactly model the points from the table.\n(c) use the model to find the future value of this investment at the end of the 7th year.\nthe future value of this investment at the end of the 7th year is $4260.\nis this an interpolation or an extrapolation from the data?\na. extrapolation\nb. interpolation\n(d) should this model be interpreted discretely or continuously?\na. discretely, because the simple interest is calculated yearly\nb. continuously, because the simple interest is calculated continuously

if $3000 is invested at 6% 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).\n|year (t)|0|1|2|3|4|5|\n|future value (s)|3000|3180|3360|3540|3720|3900|\n(a) s = 180t + 3000 (type an equation.)\n(b) a linear model cannot exactly model the points from the table.\n(c) use the model to find the future value of this investment at the end of the 7th year.\nthe future value of this investment at the end of the 7th year is $4260.\nis this an interpolation or an extrapolation from the data?\na. extrapolation\nb. interpolation\n(d) should this model be interpreted discretely or continuously?\na. discretely, because the simple interest is calculated yearly\nb. continuously, because the simple interest is calculated continuously

Answer

Explanation:

Step1: Recall simple - interest formula

The simple - interest formula is $S = P+Prt$, where $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the time in years. Given $P = 3000$ and $r=0.06$, then $S=3000 + 3000\times0.06t=180t + 3000$.

Step2: Find future value at $t = 7$

Substitute $t = 7$ into the formula $S=180t + 3000$. So $S=180\times7+3000=1260 + 3000=4260$.

Step3: Determine interpolation/extrapolation

The table shows values for $t = 0$ to $t = 5$. Since $t = 7$ is outside this range, it is an extrapolation.

Step4: Interpret the model

Simple interest is calculated yearly in this case. So the model should be interpreted discretely.

Answer:

(c) The future value of this investment at the end of the 7th year is $4260$. It is an extrapolation (A. Extrapolation). (d) A. Discretely, because the simple interest is calculated yearly.