Question

NEED HELP ASAP! Please help I need to show my work

10. The half-life of a radioactive substance is the amount of time required for half of a given sample
to decay. A container holds 1000 grams of a certain substance that has a half-life of one year.
Approximately how many grams of the substance will remain in the container after 10 years?
Hint: D= P(1-r)t
Where D is the amount of the quantity after t years
P is the initial amount
r is the percent decrease expressed as a decimal (0.5)
t is the number of years.

Answer 1

Approximately 1 gram of the substance will remain after 10 years

Explanation:

Using the given formula,

D = P(1-r)t,

This is the wrong formula, for half life, t should be the exponent of (1-r)

so,

D = P(1-r)^t

i.e. we half the amount or multiply by 0.5 each year, so, for ten years, we half the amount 10 times and so on

here, P = 1000 g

now, t = 10 years,

so,

D = (1000)(1-0.5)^(10)

D = 1000(0.5)^(10)

D = 0.9766 g

or approximately 1 gram