A lab currently has 70 mg of radioactive material that decays at 3.5% per year. Federal regulation for the substance says that the material must be safely stored until it reaches its half-life, at which time the material can be disposed. How many years will the lab have to safely

store the material before disposal?

The lab will have to wait 19.45 yers to safely store the material before disposal.

Step-by-step explanation:

Exponential equation for substance decay:

A exponential equation for the amount of a substance after t years is given by:

In which A(0) is the initial amount and r is the decay rate, as a decimal.

Decays at 3.5% per year.

This means that

So

How many years will the lab have to safely store the material before disposal?

It needs to reach half-life, that is, t for which A(t) = 0.5A(0). So

The lab will have to wait 19.45 yers to safely store the material before disposal.

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm

a

explanation: