Question

How long will Iot take 7* 1.014ᵗ to double.

Answer 1

It will take approximately 68.4 time units for the expression 7 * 1.014ᵗ to double.

Step-by-step explanation:

The formula for exponential growth is given by the equation A = P * (1 + r)^t, where A is the final amount, P is the initial amount, r is the growth rate per time period, and t is the number of time periods. In this case, we want to find the time it takes for the expression 7 * 1.014^t to double. Set A to be twice the initial value (2 * 7 = 14) and P to be 7. Also, r is 1.014.

`14=7 * (1+1.014) ^t`

Now, solve for t:

`2=1.014^t`

Taking the logarithm base 1.014 of both sides:

`t=log_(1.014)2/log_(1.014) = 68.4`

So, it will take approximately 68.4 time units for the expression to double.