Question

Element X is a radioactive isotope such that its mass decreases by 62% every year. If an experiment starts out with 650 grams of Element X, write a function to represent the mass of the sample after
t
t years, where the daily rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per day, to the nearest hundredth of a percent.

Answer 1

Use the general formula for decay substance

$\\ \rm\Rrightarrow N=N_o(1-r)^t$

• r is rate of decay.
• t is time

For our equation r=62%=0.62

So

function becomes

$\\ \rm\Rrightarrow N=650(1-0.62)^t$

$\\ \rm\Rrightarrow N=650(0.38)^t$

Change for a year

$\\ \rm\Rrightarrow N=650(0.38)$

$\\ \rm\Rrightarrow N=247g$

Amount decayed=650-247=403g

Daily decay

• 403/365
• 1.1g

Percentage decay

$\\ \rm\Rrightarrow \dfrac{1.1}{650}\times 100$

$\\ \rm\Rrightarrow 0.169$

$\\ \rm\Rrightarrow 16.9\%$