An unknown radioactive element decays into non-radioactive substances. in 440 days the radioactivity of a sample decreases by 74 percent.

(a) what is the half-life of the element?
half-life: (days)

(b) how long will it take for a sample of 100 mg to decay to 91 mg?
time needed: (days)

a) The half life of the element is 231 days.

b) It is going to take around 31.5 days for a sample of 100 mg to decay to 91 mg.

Step-by-step explanation:

The radioactivity of the sample can be modeled by the following exponential equation:

In which t is the time in days, r is the decay rate and is the initial radioactive percentage.

We have that:

In 440 days the radioactivity of a sample decreases by 74 percent.

This means that .

This helps us find r.

Applying ln to both sides.

(a) What is the half-life of the element?

This is t when

Again, we apply ln to both sides of the equality.

The half life of the element is 231 days.

(b) How long will it take for a sample of 100 mg to decay to 91 mg?

This is t when

It is going to take around 31.5 days for a sample of 100 mg to decay to 91 mg.

send it over

step-by-step explanation:

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls