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.