Question

What is the amount of a radioactive substance left at the end of year 4 if it initially started with 150,000 grams and decays at a rate of 1% per month?

A) 94,902.44 grams
B) 96,041.23 grams
C) 98,052.00 grams
D) 99,223.54 grams

Answer 1

The amount of the radioactive substance left at the end of year 4 is approximately 96,041.23 grams.

Step-by-step explanation:

To find the amount of the radioactive substance left at the end of year 4, we can use the formula for exponential decay. The formula is given by:

Amount remaining = Initial amount × (1 - decay rate)number of time periods

Given that the initial amount is 150,000 grams and the decay rate is 1% per month, we need to calculate the number of time periods. Since there are 12 months in a year, the number of time periods for 4 years is 4 × 12 = 48 months. Plugging in the values into the formula, we get:

Amount remaining = 150,000 × (1 - 0.01)48 = 96,041.23 grams

Therefore, the amount of the radioactive substance left at the end of year 4 is approximately 96,041.23 grams.