Question

one type of strontium has a radioactive decay rate of 1.4% per day. if 50 pounds of this strontium is available today, how much will still remain after 50 days? use $y = 50(0.986)^x$, and let $x$ be 50.

after 50 days, \\(\square\\) lb of strontium will still remain.
(round to the nearest hundredth as needed.)

Explanation:

Step1: Identify the formula and values

The formula for radioactive decay is given as \( y = 50(0.986)^x \), where \( x = 50 \) (number of days), and the initial amount is 50 pounds.

Step2: Substitute \( x = 50 \) into the formula

Substitute \( x = 50 \) into \( y = 50(0.986)^{50} \). First, calculate \( 0.986^{50} \). Using a calculator, \( 0.986^{50}\approx0.49696 \).

Step3: Multiply by the initial amount

Multiply the result by 50: \( y = 50\times0.49696 = 24.848 \). Round to the nearest hundredth, we get \( y\approx24.85 \).

Answer:

24.85