Question

Number 17 please and thank you . I don’t understand it . Do you plug in each 10-50 as T into your calculator?

Answer 1

The half-life for such a substance is the time $t$ required to have the amount (in grams $\mathrm g$) at time $t$ (in seconds $\mathrm s$), $y(t)$, decay to half the starting amount $y_0$. In other words, for krypton-91, after 10 seconds we would have $y(10\,\mathrm s)=\dfrac{y_0}2$. We can use this information to solve for $k$, then plug in various values of $t$ to find the amount of krypton-91 that's left...

But we don't need to! We already know it takes 10 seconds for half of the substance to decay. So if we start with 16 grams, then after 10 seconds, 8 grams will remain.

10s later (after a total of 20 seconds), 4g will remain.

10s later (30s), 2g will remain.

10s later (40s), 1g will remain.

10s later (50s), 1/2 g will remain.