Question

The number of grams A of a certain radioactive substance present at time t is given by the formula A=25e^(−0.00032t), where t is the number of years from the present. How many grams are present initially? How many grams are present after 1000 years? What is the half-life of this substance?

a. Initial grams: 25g, After 1000 years: 15.88g, Half-life: 2160.42 years
b. Initial grams: 25g, After 1000 years: 10.62g, Half-life: 2160.42 years
c. Initial grams: 32g, After 1000 years: 25g, Half-life: 2160.42 years
d. Initial grams: 32g, After 1000 years: 15.88g, Half-life: 2160.42 years

Answer 1

The initial grams of the radioactive substance are 25g, the grams present after 1000 years are 15.88g, and the half-life is approximately 2160.42 years.

Step-by-step explanation:

The formula for the number of grams A of a certain radioactive substance present at time t is given by the equation A = 25e^(-0.00032t), where t is the number of years from the present.

To find the initial grams, we can substitute t = 0 into the equation: A = 25e^(-0.00032 * 0) = 25e^0 = 25 grams.

To find the grams present after 1000 years, we can substitute t = 1000 into the equation: A = 25e^(-0.00032 * 1000) ≈ 15.88 grams.

The half-life of a substance can be found by solving for t when A = (1/2) * initial grams. Using the equation (1/2) * 25 = 25e^(-0.00032t), we can solve for t, and we get a half-life of approximately 2160.42 years.