Question

A 30-gram sample of bacteria has some unknown disease that is killing the bacteria. The amount of bacteria is measured each day and the results are shown in the table. Number of Days (d) Amount of Bacteria in Grams (A) 0 30 1 28.5 2 27.075 3 25.72 4 24.44 5 23.21 6 22.05 What is the decay factor of this data? a. Decay factor is 0.95 b. Decay factor is -1.5 c. Decay factor is 14.25 d. Decay factor is 0.05

Answer 1

For this case we have an equation of the form:
 y = A * (b) ^ t
 Where,
 A: initial amount
 b: decrease factor
 t: time
 Substituting values:
 y = 30 * (b) ^ t
 To calculate t we use a point in the table.
 We have:
 (t, y) = (1, 28.5)
 Substituting:
 28.5 = 30 * (b) ^ 1
 b = 28.5 / 30
 b = 0.95
 Answer:
 a. Decay factor is 0.95

Answer 2

The decay factor of the given data in the table is gotten as; A: 0.95

How to find the decay factor?

The equation to find the decay factor is;

y = A(b)^t

Where;

A is initial amount

b: is decay factor

t is time

From the question, the initial amount of bacteria is 30. Thus, A = 30

To find the decay factor, let us use a point on the table. We will use the second point which is; (1, 28.5)

Thus;

28.5 = 30 × b¹

b = 28.5/30

b = 0.95

Thus, the Decay factor = 0.95

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