Question 185318
In this question we will have to use the Continuously Compounded Interest Formula which is represented by the equation {{{A = Pe^(r*t)}}} where A is the resulting number, P is the original number, r is the rate, and t is the time.
-----
In this question we have an original value of 800 grams, and an ending value of 85 grams so we can set up the equation like this:
{{{85 = 800*e^(-0.032*t)}}}
Since we are trying to find how long it will take, we are trying to solve for t (time). To get a variable out of the exponent we will have to take the logarithm of both sides after the problem is simplified.
{{{.10625 = e^(-0.032*t)}}} (Divide both sides by 800)
{{{ln(.10625) = ln(e^(-0.032*t))}}} (Take the natural log of both sides, log base e)
{{{ln(.10625) = -0.032*t}}} (Use the logarithm power property to take the exponent out)
{{{-ln(.10625)/0.032 = t}}} (Divide both sides by -0.032)
{{{t = 70.0612647243003387}}} (Solve the natural log with a calculator)
{{{t = 70 years}}} (Round to the nearest number of years)