Question

A sample of 600 g of an isotope decays to another isotope according to the function A(t) = 600e⁻⁰.⁰⁴⁹ᵗ where t is the time in years.

(a) How much of the initial sample will be left in the sample after 20 years?

Answer 1

After 20 years, approximately 225.18 grams of the initial isotope will be left in the sample, calculated using the decay function A(t) = 600e^{-0.049t}.

Step-by-step explanation:

To determine how much of the initial isotope will be left after 20 years, we can use the given function A(t) = 600e−0.049t, where A(t) is the amount of isotope remaining at time t in years. We can find out how much remains after 20 years by plugging in t = 20 into our function:

A(20) = 600e−0.049(20)

Calculating the exponent:

e−0.049(20) = e−0.98 ≈ 0.3753

Now, multiply this by the initial amount:

A(20) = 600 × 0.3753 ≈ 225.18 g

So, after 20 years, approximately 225.18 g of the initial isotope will be left in the sample.