Please see the photo, where $PV(D,t)$ the the value in present$-$day dollars of the promise of $D$ dollars to be paid in $t$ years,

where $t$ and $D$ are any non$-$negative real numbers.

$($a$)$ Recall the model is only used with positive values of $D.$

i$.***\sqrt[\phantom{2}]{2}tt$ Interpret $\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{t}}[PV]<mn\; id="EditorElement\_16985532">0</mn>$ in terms of the model.

ii$.******$ Now, interpret $\frac{de{l}^{2}PV}{del{t}^2}>0.$ Select the best interpretation below. For this part, you

do not need to justify your answer.

A$.$ The rate at which future income loses value over time decreases. For example: the

difference between a dollar today and a dollar next year is greater than the difference

between a dollar in two years and a dollar in three years.

B$.$ The rate at which future income loses value over time increases. For example: the

difference between a dollar today and a dollar next year is less than the difference

between a dollar in two years and a dollar in three years.

C$.$ The rate at which future income loses value over time is constant. For example: the

difference between a dollar today and a dollar next year is the same as than the

difference between a dollar in two years and a dollar in three years.