Question

Question #653bd

Answer 1

`t = 13.67`.

Explanation:

This is, at first, a tricky question. However, once you learn, this type of question is easy to do. I will divide it into steps:

1. We start with `2=[1+(0.052/1)]^t`. We will use logarithms to solve this. We'll put a 'log' on both sides to start with: `log(2) = log([1+(0.052/1)]^t)`.
2. We are going to use a basic log 'trick'. As we know, we can put a power as a multiplication, such that `log(2) = log([1+(0.052/1)]^t)` turns into `log(2) = t*log([1+(0.052/1)])`.
3. Now, we will simply divide in order to leave '`t`' alone. So, we pass `log([1+(0.052/1)])` from the right side, where it is multiplying, to the left side, therefore dividing. We end up with:
   `t = (log(2)) / log([1+(0.052/1)])`.
4. Now, we simply put those values in the calculator and... Ta ra! We get the answer.
   `t = 13.67` to 2 decimal points.

Tip: If you put your operations in between Hashtags/Sharps (#) these will convert from Line Format to Math Format

Hope it Helps! :D .