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.
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M(t) = ?
minutes=?

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

t ≅ 55 (rounding to the nearest minute)

jainveenamrata jainveenamrata · Answer 2 · 2022-03-23T14:37:54+01:00

The exponential equation is [tex]\rm M = 10^7\ * 2^{\frac{t}{20}}[/tex]. And the time is taken to get 67 million is 54.88 minutes.

What is an exponent?

Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

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.

The exponential equation will be given as

[tex]\rm M = 10^7\ * 2^{\frac{t}{20}}[/tex]

M be the total number of bacterial microbes in millions, as a function of time (t).

The population of the bacteria is 67 million then the time will be

[tex]\rm 67*10^6 = 10^7\ * 2^{\frac{t}{20}}\\\\2^{t/20} = 6.7[/tex]

Taking log both sides, we have

[tex]\rm \dfrac{t}{20} *log\ 2 = log \ 6.7\\\\t = 54.88[/tex]

More about the exponent link is given below.

https://brainly.com/question/5497425