Question

Using A(t)=500(1.6)^t. When will the starting amount of 500 be doubled?

Answer 1

Answer: $\frac{ln 2}{ln 1.6 }$, or ~1.4747 $t$. You didn't specify a unit for t, so if that is days, months, or years, that is the amount of specified time.

Step-by-step explanation:

To calculate how long it will take to double, you need to solve for the variable $t$.

To do this, insert the doubled value of 500 where $A(t)$ currently is.

$1000 = 500(1.6)^{t}$

Then, simplify the equation by dividing each side by 500.

$2 = (1.6)^{t}$

Then, take the logarithm of both sides.

㏑2 = ㏑(1.6)^t

Using the rule of logarithms, you can simplify this further:

㏑2 = t * ㏑1.6

Next, you can divide each side by ㏑1.6. This is your final answer.

You can simplify this further by dividing the logarithms.