Question

an unknown material decays at a continuous rate of 17.2% per day. using exponential functions, determine how much will 112 mg of the material decay to in 3 days? round to 2 decimal places, where necessary. a(3) ≈

Explanation:

Step1: Identify the formula for continuous decay

The formula for continuous decay is \(A(t)=A_0e^{-rt}\), where \(A_0\) is the initial amount, \(r\) is the decay rate, and \(t\) is the time.

Step2: Substitute the given values into the formula

Given \(A_0 = 112\) mg, \(r=0.172\), and \(t = 3\).

$$
LATEXBLOCK0
$$

Step3: Calculate the value of \(e^{-0.516}\)

Using a calculator, \(e^{-0.516}\approx0.5969\)

Step4: Calculate \(A(3)\)

$$
LATEXBLOCK1
$$

Answer:

\(66.85\)