Question

a radioactive substance has an initial mass of 100 grams and its mass halves every 4 years. Which expression shows the number of grams remaining after t years?

1) 100(4)^t/4
2) 100(4)^-2t
3)100(1/2)^t/4
4)100(1/2)^4t

Answer 1

We start with a mass of

$100 = 100 \cdot \left(\dfrac{1}{2}\right)^0$

After 4 years, we have

$50= 100 \cdot \left(\dfrac{1}{2}\right)^1$

After 8 years, we have

$25= 100 \cdot \left(\dfrac{1}{2}\right)^2$

So, as you can see, the general formula is

$m = 100 \cdot \left(\dfrac{1}{2}\right)^{\frac{t}{4}}$

Answer 2

The correct answer is option 3 which is  $N= 100(\dfrac{1}{2})^\frac{t}{4}$.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

• A radioactive substance has an initial mass of 100 grams and its mass halves every 4 years.

The expression will be calculated as:-

For 0 years expression is

$N= 100(\dfrac{1}{2})^0$

For the next 4 years, it will be:-

$N= 100(\dfrac{1}{2})^2$

For t years it will be:-

$N= 100(\dfrac{1}{2})^\frac{t}{4}$

Therefore the correct answer is option 3 which is  $N= 100(\dfrac{1}{2})^\frac{t}{4}$.

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