Question

The profit of a small scale company grows exponentially So that the initial amount has doubled In 3hours. How many times the initial amount of money will be present after 9 hours

Answer 1

The profit grows exponentially

$$P(t)=P_0e^{kt}$$

The initial amount has doubled In 3hours

$$P(3)=P_0e^{k(3)}=2P_0$$

$$3k=\ln2$$

$$k=\dfrac{1}{3}\ln2$$

Then

$$P(t)=P_02^{t/3}$$

$$P(9)=P_02^{9/3}=8P_0$$

The initial amount of money will be 8 times itself in 9 hours.