Question

Suppose the quantity (in grams) of a radioactive substance present at time t is

Q(t)= 1,000(5⁻⁰.³ᵗ) where t is a time in month.
A. How much will be present in 6 months?
B. How long will it take to reduce the substance to 8g?

Answer 1

To find how much will be present in 6 months, substitute t = 6 into the given equation. To find how long it will take to reduce the substance to 8 grams, set Q(t) = 8 and solve for t.

Step-by-step explanation:

A. To find how much will be present in 6 months, we need to substitute t = 6 into the equation Q(t) = 1,000(5^(-0.3t)).

Q(6) = 1,000(5^(-0.3*6))

Q(6) = 1,000(5^(-1.8))

Q(6) = 1,000(0.066) ≈ 66 grams

Therefore, approximately 66 grams will be present in 6 months.

B. To find how long it will take to reduce the substance to 8 grams, we need to set Q(t) = 8 and solve for t.

8 = 1,000(5^(-0.3t))

Divide both sides by 1,000: 0.008 = 5^(-0.3t)

Take the logarithm of both sides: log5(0.008) = -0.3t

Use logarithm properties to solve for t: t = -log5(0.008) / 0.3 ≈ 19.6 months

Therefore, it will take approximately 19.6 months to reduce the substance to 8 grams.