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.

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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