Ascientist runs an experiment involving a culture of bacteria. she notices that the mass of the bacteria in the culture increases exponentially with the mass increasing by 246% per week. (a) what is the 1-week growth factor for the mass of the bacteria? (b) what is the 1-day growth factor for the mass of the bacteria? (c) by what percent does the mass of bacteria increase by each day? (d) if the mass of the bacteria instead increased by 433% per week, by what percent would the mass increase by each day?

Since, the exponential growth function,

Where,

P = initial value,

t = number of periods

r = rate of increasing per period

1 + r = Growth factor per period,

(a) Here, rate of increasing per week r = 246% = 2.46,

So, the 1-week growth factor = 1 + 2.46 = 3.46

(b) Since, number of days in a week = 7,

So, the growth rate per day = ≈ 0.35

Thus, the 1-day growth factor for the mass of the bacteria = 1 +0.35 = 1.35

(c) ∵ the growth rate per day = 0.35 = 35%,

That is, the mass of bacteria increase by 35% each day ( approx )

(d) If the rate of increasing per week r = 433% = 4.33 ,

Then the rate of increasing mass per day = ≈ 0.62 = 62%

Hence,  62% would the mass increase by each day.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

1.) 21

2.) 0.453

3.) 1.5

4.) 48

5.) $ 22

step-by-step explanation: