Question

a type of radioactive element has a daily radioactive decay rate of 0.6%. if 16 pounds of this element are available today, find how much will still remain after 70 days. use an exponential decay model of the form $y = y_0e^{-kcdot t}$, where $k$ is the decay rate. if needed, enter your answer to 5 decimal places.
$y=\text{ }$pounds.

Explanation:

Step1: Identify the values of $y_0$, $k$, and $t$

$y_0 = 16$ (initial amount), $k=0.006$ (0.6% as a decimal), $t = 70$ (number of days)

Step2: Substitute values into the formula

$y=y_0e^{-k\cdot t}=16e^{-0.006\times70}$

Step3: Calculate the exponent

$-0.006\times70=- 0.42$

Step4: Calculate the value of $e^{-0.42}$

Using a calculator, $e^{-0.42}\approx0.65704$

Step5: Calculate the final amount $y$

$y = 16\times0.65704 = 10.51264$

Answer:

$10.51264$