Question

The half-life of a substance is four days. A sample of the substance has an initialweight of 100 kilograms. The decay is described by a formula where x is thenumber of days and y is the weight of the sample in kilograms.Which equation and graph represent the weight of the described sample of thesubstance over time?

Answer 1

The half-life of a substance is the amount of time it takes for it to decrease to half of its initial value.

So, using y for the weight after x days, we can represent this decay function as:

`y=y_0((1)/(2))^{(x)/(4)}`

where y₀ is the initial weight.

Notice that when t = 4 this function is given by

`y(4)=y_0((1)/(2))^{(4)/(4)}=(y_0)/(2)`

Although this question doesn't provide information about the initial weight, all the available options present it as 100. So, the equation that represents the weight of the described sample of the substance over time is

`y=100((1)/(2))^{(x)/(4)}`

Therefore, the second option is correct.