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A population of bacteria is growing according to the equation P(t) = 1650e ^0.11t. Estimate when the population will exceed 2270.

t = ________

User Soatl
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Final answer:

By rearranging the exponential growth equation P(t) = 1650e^0.11t to solve for t and performing calculations, it is estimated that the bacterial population will exceed 2270 after approximately 23.87 time units.

Step-by-step explanation:

To estimate when the population of bacteria will exceed 2270, we can set the equation P(t) = 1650e ^0.11t to be greater than 2270 and solve for t. We can rearrange the equation to solve for t by first dividing both sides by 1650 to isolate the exponential expression.

2270 / 1650 = e0.11t

Then, we take the natural logarithm (ln) of both sides to solve for t:

ln(2270 / 1650) = ln(e0.11t)

ln(2270 / 1650) = 0.11t

Now, divide by 0.11 to find t:

t = ln(2270 / 1650) / 0.11

By performing the calculations, we'll get the approximate value for t, which represents the time in units at which the population of bacteria will exceed 2270.

Let's calculate:

t ≈ ln(1.37576) / 0.11

t ≈ 2.6254752 / 0.11

t ≈ 23.86705

Therefore, the estimated time when the population will exceed 2270 is approximately 23.87 time units.

User Qiniso
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