NEED HELP ASAP PLEASE!!
A bacteria culture starts with 2000 bacteria and the population doubles every 3 hours.
a) A function that models the number of bacteria after t hours is p(t)=____________?
b) The number of bacteria present after 5 hours will be about _____ ?
c) The population will reach 22000 after approximately ________ hours.
very similar to your
http://www.jiskha.com/display.cgi?id=1267744260
except we have
p(t) = 2000(2)^t, where t is the number of 3-hour periods.
a) To find a function that models the number of bacteria after t hours, we need to know the initial number of bacteria and how the population changes over time. In this case, we know that the population doubles every 3 hours.
If we start with 2000 bacteria, after 3 hours, we will have 2000 * 2 = 4000 bacteria. After 6 hours, we will have 4000 * 2 = 8000 bacteria.
Based on this pattern, we can say that the number of bacteria after t hours is given by the function p(t) = 2000 * 2^(t/3).
b) To find the number of bacteria present after 5 hours, we will substitute t = 5 into the function p(t) that we found in part (a):
p(5) = 2000 * 2^(5/3)
≈ 2000 * 2^(1.67)
≈ 2000 * 5.63
≈ 11,260 (rounded to the nearest whole number)
So, the number of bacteria present after 5 hours will be about 11,260.
c) To find the time it takes for the population to reach 22000 bacteria, we need to solve the equation p(t) = 22000.
22000 = 2000 * 2^(t/3)
To solve for t, we can divide both sides of the equation by 2000:
11 = 2^(t/3)
Now, we need to take the logarithm of both sides to isolate t:
log(11) = log(2^(t/3))
Using the property of logarithms that states log(a^b) = b * log(a), we can rewrite the equation as:
log(11) = (t/3) * log(2)
Now, we can solve for t by multiplying both sides by 3 and then dividing by log(2):
t = (3 * log(11)) / log(2)
Using a calculator to evaluate the expression, we find:
t ≈ 10.21 (rounded to two decimal places)
So, the population will reach 22000 after approximately 10.21 hours.