Your monthly profit p on sales of Avocado Ice Cream are rising at an instantaneous rate of 17% per month. If you currently make a profit of $14,500 per month, solve the differential equation that describes your change in profit to predict your monthly profits. Assume that the current sales are given for time $t = 0$ .
A) $s = 14,500 e ^ { - 0.17 t }$ .
B) $s = 14,500 e ^ { - 1.7 t }$
C) $s = 14,500 e ^ { - 0.17 t }$
D) $s = 14,500 + e ^ { - 0.17 t }$
E) $s = 14,500 + t ^ { 0.17 }$

Question

Your monthly profit p on sales of Avocado Ice Cream are rising at an instantaneous rate of 17% per month. If you currently make a profit of $14,500 per month, solve the differential equation that describes your change in profit to predict your monthly profits. Assume that the current sales are given for time $t = 0$ .  
A) $s = 14,500 e ^ { - 0.17 t }$ .
B)   $s = 14,500 e ^ { - 1.7 t }$
C)    $s = 14,500 e ^ { - 0.17 t }$
D)   $s = 14,500 + e ^ { - 0.17 t }$
E)   $s = 14,500 + t ^ { 0.17 }$

Quizplus · Accepted Answer

The differential equation is:$$\frac{dp}{dt} = 0.17p$$Solving this equation gives:$$p = Ce^{0.17t}$$Using the initial condition, we get:$$14500 = Ce^0$$$$C = 14500$$Therefore, the solution to the differential equation is:$$p = 14500e^{0.17t}$$

Your Monthly Profit P on Sales of Avocado Ice Cream t=0t = 0t=0

Your Monthly Profit P on Sales of Avocado Ice Cream $t = 0$