Answer:
<u>M(t) = 6.7 * 10⁷ (67 million)</u>
<u>Minutes (t) =55</u>
Step-by-step explanation:
1. Write an exponential equation that represents M, the total number of bacterial microbes in millions, as a function of t, the number of minutes the sample has been observed.
For answering this question, we will use the following formula:
M(t) = B₀ * g ^(t/m), where:
- M(t) represents the total number of bacterial microbes in millions.
- B₀ represents the initial population of bacteria in millions.
- g represents the growth factor.
- t represents the total number of minutes we will observe the bacteria growing.
- m represents the time in minutes it takes to the growth factor g to occur.
2. Then, determine how much time, to the nearest minute, will pass until there are 67 million bacterial microbes.
M(t) = B₀ * g ^(t/m)
Replacing with the values we know:
6.7 * 10⁷ = 10⁷ * 2 ^(t/20)
6.7 = 2 ^(t/20) (Dividing by 10⁷ at both sides)
ln 6.7 = ln 2 ^(t/20)
ln 6.7 = t/20 ln 2
ln 6.7/ ln 2 = t/20
t = ln 6.7/ln 2 * 20
t = 2.74 * 20
t = 54.88
<u>t ≅ 55 (rounding to the nearest minute)</u>
