The number of cells in a petri dish doubles every hour according to the equation N(t) = 50(2)t where represents the number of cells after t hours.
If there are 61440 cells in the dish, how much time has passed (round to nearest hour)?
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hours
If there are 983040 cells in the dish, how much time has passed (round to nearest hour)?
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hours
To find the time that has passed when there are 61440 cells in the dish, we can substitute 61440 for N(t) in the equation N(t) = 50(2)^t and solve for t:
61440 = 50(2)^t
Divide both sides of the equation by 50:
61440/50 = (2)^t
1228.8 = (2)^t
Take the logarithm of both sides of the equation to isolate t:
log(1228.8) = t * log(2)
Using a calculator, we find that log(1228.8) ≈ 3.089
Now, divide both sides of the equation by log(2):
t = 3.089 / log(2)
t ≈ 10.62
Rounding to the nearest hour, approximately 11 hours have passed.
To find the time that has passed when there are 983040 cells in the dish, we can use the same process:
983040 = 50(2)^t
Divide both sides of the equation by 50:
983040/50 = (2)^t
19660.8 = (2)^t
Take the logarithm of both sides of the equation:
log(19660.8) = t * log(2)
Using a calculator, we find that log(19660.8) ≈ 4.295
Now, divide both sides of the equation by log(2):
t = 4.295 / log(2)
t ≈ 14.95
Rounding to the nearest hour, approximately 15 hours have passed.