Question

In: Advanced Math

Rounding to six significant digits, write an exponential equation representing this situation. To the nearest minute...For the following exercises, use this scenario: A biologist recorded a count

For the following exercises, use this scenario: A biologist recorded a count of 360 bacteria present in a culture after 5 minutes and 1,000 bacteria present after 20 minutes.

Rounding to six significant digits, write an exponential equation representing this situation. To the nearest minute, how long did it take the population to double?

Expert Solution

Consider that a biologist recorded a count of 360 bacteria present in a culture after 5 minutes and 1000 bacteria present after 20 minutes. The initial population in the culture was 256.

Suppose that population count of bacteria after t minutes is

P(t) = 256ert

Therefore,

360 = 256er(5)

er(5) = 1.40625

r = 1/5ln(1.40625)

r = 0.068185

Hence, the population count of bacteria after t minutes is

P(t) = 256e0.068185t

Put P(t) = 2(256)

Therefore,

2(256) = 256e0.068185t

256e0.068185t = 2

t = ln(2)/0.068185

t ≈ 10

Hence, it takes 10 minutes the population to double.

Junaid answered 1 year ago

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