A scientist has a sample of bacteria that initially contains 10 million microbes. He observes the sample
and finds that the number of bacterial microbes doubles every 20 minutes. 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. Then, determine how much time, to the nearest minute, will pass
until there are 67 million bacterial microbes.
Enter your answers in the boxes. Enter only your answers.
M(t) = ?
minutes=?

M(t) = 6.7 * 10⁷ (67 million)

Minutes (t) =55

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:

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

t ≅ 55 (rounding to the nearest minute)

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step-by-step explanation:

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