If a sample of 120 grams decays to only 85 grams after 6 days, how many grams of Mathonite will remain after 12 days?

Question

Problem about exponential decay.

Answer 1

y = 120e^kt

 

When t = 6, y = 85.  So, 85 = 120e^6k

 

e^6k = 0.70833333

 

6k = ln(0.7083333) = -0.3448

 

k = -0.057

 

So, y = 120e^-0.057t

 

Therefore, when t = 12, y = 120e^-0.057(12) = 60.55 g

 

Answer 2

We need to write an exponential function that describes this situation.  Exponential decay means that the graph decreases exponentially as x increases.

 

Let x = time (days)

Let y = decay (grams)

 

 

We start with the initial value of 120 grams.  After 6 days, the decay is 85 grams.

 

 

y = 120^{(-x + A)}

 

 

We want to solve for A.  Substitute y=85 and x=6.

 

85 = 120^{-6 + A}

 

 

Log both sides of the equation and bring the exponent down as the coefficient of the log.

 

Log(85) = (-6 + A)Log(120)

 

 

Divide both sides of the equation by log(120). This will isolate the A term.

 

 

0.928 = -6 + A

 

 

Add 6 on both sides of equation.

 

6.928 = A

 

 

Substitute this value back into the original function.

 

y = 120^{(-x + 6.928)}

 

 

Next, to find how many grams will remain after 12 day, just substitute x=12 into the function coded in orange.