The above is a query in my maths textbook within the subject matter Exponential increase & Decay.

i am a piece confused as to how I have to technique this query.

We have been taught to use the formula:

$$Q=A{e}^{kt}$$

Where Q is the quantity, A is the initial quantity, k is the growth/decay constant and t is the time.

In reference to the question, I don't think I need A so here is the equation I ended up with:

$$2Q={e}^{25k}$$

Edit:

I found out that

$$k=\frac{\mathrm{ln}2}{25}$$

I then let Q=3A and the following is my working:

$$3A=A{e}^{25\frac{\mathrm{ln}2}{25}t}$$

$$3A=A{e}^{\mathrm{ln}2t}$$

$$3={e}^{\mathrm{ln}2t}$$

$$3={2}^{t}$$

$$\mathrm{ln}3=t\mathrm{ln}2$$

$$t=\frac{\mathrm{ln}3}{\mathrm{ln}2}$$

$$t=1.6$$

I can't figure out what is wrong in my working out.

The provided answer is: 39.6 years