Question

1. radioactive decay results in the release of energy and matter from the nucleus of an atom. if the rate of radioactive decay for a particular substance is 3.75% per hour, how many remain after 19 hours if the initial amount was 150 grams?\

\bigcirc 89.97 grams\
\bigcirc 78.42 grams\
\bigcirc 75.39 grams\
\bigcirc 81.05 grams

Explanation:

Step1: Define decay formula

The formula for exponential decay is $A(t) = A_0(1-r)^t$, where $A_0$ = initial amount, $r$ = decay rate, $t$ = time.

Step2: Identify given values

$A_0 = 150$ grams, $r = 0.0375$, $t = 18$ hours

Step3: Substitute values into formula

$A(18) = 150(1-0.0375)^{18} = 150(0.9625)^{18}$

Step4: Calculate the decay factor

First compute $0.9625^{18} \approx 0.4598$

Step5: Find final amount

$A(18) = 150 \times 0.4598 \approx 68.97$ grams

Answer:

68.97 grams