Question

Suppose the rate of savings in Malaysia is given by

dS/dt=5.1e^t+400t^2+6000


where t is the time in years, and S is the amount of money saved in billions of RM. Find the function S(t) which gives the total amount of money saved. You may assume that RM0 is saved at t = 0.

Answer 1

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Answer on Question #63338 – Math – Calculus

Question

Suppose the rate of savings in Malaysia is given by

$$\frac{ds}{dt} = 5.1e^t + 400t^2 + 6000,$$

where $t$ is the time in years, and $S$ is the amount of money saved in billions of RM.

Find the function $S(t)$ which gives the total amount of money saved. You may assume that RMO is saved at $t = 0$.

Solution

$$\begin{array}{l} dS = (5.1e^t + 400t^2 + 600)dt \\ \int dS = \int (5.1e^t + 400t^2 + 600)dt \\ S(t) = 5.1e^t + \frac{400}{3}t^3 + 600t + C, \\ \end{array}$$

where $C$ is the initial amount of money.

**Answer:** $S(t) = 5.1e^t + \frac{400}{3}t^3 + 600t + C$.