3) A sample of 42 grams of an unknown substance has a half-life of 1,300 years. (a) Write an equation to determine the amount of substance, S, left after t years.

(b) Approximately how long will it take for 0.2 grams of substance to remain (to the nearest year)?

a)

b) It will take 10,692 years.

Step-by-step explanation:

Exponential function to determine the amount of substance:

An exponential function to determine the amout of substance after t years is given by:

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

(a) Write an equation to determine the amount of substance, S, left after t years.

Half-life of 1300 years means that .

We use this to find r. So

Sample of 42 grams means that . So

Replacing A by S, just for notation purposes

(b) Approximately how long will it take for 0.2 grams of substance to remain (to the nearest year)?

This is t when . So

It will take 10,692 years.

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation:

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,