When a radioactive substance decays, measurements of the amount remaining over constant Amount of radioactive substance remaining
intervals of time form a geometric sequence. The table shows the amount of a certain substance,
remaining after different constant intervals. Write the explicit and recursive formulas for the
Time (min)
0 100 200 300
geometric sequence formed by the amount of the radioactive substance remaining
Amount (picograms)
480 240 120 60
The explicit formula for the geometric sequence formed by the amount of the radioactive substance remaining is an-(Type your answer using exponential
notation)

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is