A scientist 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?

Answer:Since, the exponential growth function,[tex]A=P(1+r)^{t}[/tex]Where,P = initial value,t = number of periodsr = rate of increasing per period1 + 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 = [tex]\frac{2.46}{7}[/tex] ≈ 0.35Thus, 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 = [tex]\frac{4.33}{7}[/tex] ≈ 0.62 = 62%Hence,  62% would the mass increase by each day.