monthly sales of a particular personal computer are expected to decline at the following rate of s(t)…

monthly sales of a particular personal computer are expected to decline at the following rate of s(t) computers per month, where t is time in months\nand s(t) is the number of computers sold each month.\ns(t) = -20t^2/3\nthe company plans to stop manufacturing this computer when monthly sales reach 600 computers. if monthly sales now (t = 0) are 1,600 computers,\nfind s(t). how long will the company continue to manufacture this computer?\ns(0) = □

monthly sales of a particular personal computer are expected to decline at the following rate of s(t) computers per month, where t is time in months\nand s(t) is the number of computers sold each month.\ns(t) = -20t^2/3\nthe company plans to stop manufacturing this computer when monthly sales reach 600 computers. if monthly sales now (t = 0) are 1,600 computers,\nfind s(t). how long will the company continue to manufacture this computer?\ns(0) = □

Answer

Explanation:

Step1: Integrate the rate function

We know that if (S^{\prime}(t)) is the rate of change of (S(t)), then (S(t)=\int S^{\prime}(t)dt). Given (S^{\prime}(t)=-\frac{200}{3}), then (S(t)=-\frac{200}{3}t + C).

Step2: Find the constant of integration

When (t = 0), (S(0)=1800). Substitute into (S(t)=-\frac{200}{3}t + C), we get (1800=-\frac{200}{3}(0)+C), so (C = 1800). Then (S(t)=-\frac{200}{3}t+1800).

Step3: Solve for (t) when (S(t)=600)

Set (S(t)=600), so (600=-\frac{200}{3}t + 1800). First, subtract (1800) from both sides: (600 - 1800=-\frac{200}{3}t). (- 1200=-\frac{200}{3}t). Then multiply both sides by (-\frac{3}{200}): (t=\frac{-1200\times(-3)}{200}). (t = 18).

Answer:

(18)