Question

The half-life of a certain Martian substance is 90 days. Today, you have 5 lbs of that substance stored in your fridge, and it has been sitting around in there for 2 weeks. How much did it weigh back then? (2 weeks ago)

Answer 1

Explanation:

The half-life of the Martian substance is 90 days, which means that after 90 days, the initial amount of the substance will be reduced by half.

We can use this fact to find the amount of the substance 2 weeks ago. Since 2 weeks is equivalent to 14 days, the substance has gone through 14/90 of a half-life.

Let's call the initial amount of the substance "A". After 14/90 of a half-life, the amount of substance remaining is:

A * (1/2)^(14/90)

We know that the current amount of the substance is 5 lbs. So we can set up an equation:

A * (1/2)^(14/90) = 5

Solving for A:

A = 5 / (1/2)^(14/90)

A = 5.309 lbs

Therefore, 2 weeks ago, the Martian substance weighed about 5.309 lbs.

Answer 2

The half-life of a substance is the time it takes for half of the substance to decay. In this case, the half-life of the Martian substance is 90 days.

We can use the half-life formula to find the original weight of the substance:

original weight = current weight / (1/2)^(elapsed time / half-life)

where "elapsed time" is the time that has passed since the substance was last at its original weight.

In this problem, the current weight is 5 lbs, the elapsed time is 2 weeks, or 14 days, and the half-life is 90 days.

First, we need to convert the elapsed time to days:

2 weeks = 14 days

Now we can plug in the values into the formula:

original weight = 5 / (1/2)^(14/90)

Simplifying the exponent, we get:

original weight = 5 / (1/2)^(7/45)

Using the fact that (1/2)^2 = 1/4, we can simplify further:

original weight = 5 / (1/4)^(7/180)

original weight = 5 / 0.843

original weight = 5.93 lbs (approximately)

Therefore, the substance weighed approximately 5.93 pounds 2 weeks ago.