Question

for the following table, compute the mass of 1,440 grams of radioactive element d left each day if element d loses half its mass every day. what type of decay is this?

day | mass (g)
1 | 1,440
2 |
3 |
4 |
5 |

complete the table

day | mass (g)
1 | 1,440
2 | 720
3 | 360
4 | 180
5 | 90

what type of decay is this?

it is dropdown decay

exponential

linear

Explanation:

For the table completion (calculating the mass each day):

Step 1: Understand the decay rule

The element loses half its mass each day, so the mass on day \( n \) is \( \text{Mass on day } n - 1 \times \frac{1}{2} \).

Step 2: Calculate mass on day 2

Mass on day 1: \( 1440 \) g.
Mass on day 2: \( 1440 \times \frac{1}{2} = 720 \) g.

Step 3: Calculate mass on day 3

Mass on day 2: \( 720 \) g.
Mass on day 3: \( 720 \times \frac{1}{2} = 360 \) g.

Step 4: Calculate mass on day 4

Mass on day 3: \( 360 \) g.
Mass on day 4: \( 360 \times \frac{1}{2} = 180 \) g.

Step 5: Calculate mass on day 5

Mass on day 4: \( 180 \) g.
Mass on day 5: \( 180 \times \frac{1}{2} = 90 \) g.

For the type of decay:

Radioactive decay where the quantity decreases by a constant factor (here, \( \frac{1}{2} \)) over equal time intervals is exponential decay. Linear decay would involve a constant decrease in mass (e.g., losing a fixed grams per day), but here the decrease is proportional to the current mass (losing half each day), so it is exponential.

Answer:

For the table:
Day 2: \( 720 \) g, Day 3: \( 360 \) g, Day 4: \( 180 \) g, Day 5: \( 90 \) g.

For the decay type: exponential