Question

There are five parts to this problem. The amount left after 10 seconds is blank grams.

Answer 1

ANSWERS

• After ,10, seconds: ,88 grams

,

• After ,20, seconds: ,44 grams

,

• After ,30, seconds: ,22 grams

,

• After ,40, seconds: ,11 grams

,

• After ,50, seconds: ,5.5 grams

EXPLANATION

The amount of substance remaining is,

$N(t)=N_o\left(\frac{1}{2}\right)^{t/h}$

Where N₀ is the initial quantity of the substance, h is the half-life of the substance, t is the time and N(t) is the quantity remaining.

In this case, the initial quantity, N₀, is 176 grams and the half-life, h, is 10 seconds, so we have the formula,

$N(t)=176\left(\frac{1}{2}\right)^{t/10}$

And we have to find N(10), N(20), N(30), N(40), and N(50):

$N(10)=176\left(\frac{1}{2}\right)^{10/10}=176\cdot\frac{1}{2}=88$$N(20)=176\left(\frac{1}{2}\right)^{20/10}=176\cdot\frac{1}{2^2}=176\cdot\frac{1}{4}=44$$N(30)=176\left(\frac{1}{2}\right)^{30/10}=176\cdot\frac{1}{2^3}=176\cdot\frac{1}{8}=22$$N(40)=176\left(\frac{1}{2}\right)^{40/10}=176\cdot\frac{1}{2^4}=176\cdot\frac{1}{16}=11$$N(50)=176\left(\frac{1}{2}\right)^{50/10}=176\cdot\frac{1}{2^5}=176\cdot\frac{1}{32}=5.5$

Hence, the amount of substance remaining after each period of time is:

• 10, seconds: ,88 grams

,

• 20, seconds: ,44 grams

,

• 30, seconds: ,22 grams

,

• 40, seconds: ,11 grams

,

• 50, seconds: ,5.5 grams