The formula N = 10(4') gives N, the number of bacteria present in a culture after t hours. How many hours
does it take for the number of bacteria to grow to 2,560?
a. 2 hours
b. 3 hours
c. 4 hours
d. 5 hours
The answer is c., but is there another way to find this answer besides substituting?
Yes, there is another way to find the answer without directly substituting values into the equation.
The formula N = 10(4') represents exponential growth, where the bacteria population doubles every t hours. In this case, the initial number of bacteria is 10, and the growth factor is 4.
To find the number of hours it takes for the number of bacteria to grow to 2,560, we can set up an equation:
2,560 = 10(4')
Now, let's try to simplify the equation further. Since 2,560 is equal to 10 times some value (4'), we can divide both sides of the equation by 10:
2,560 / 10 = 4'
This simplifies to:
256 = 4'
Now, in exponential notation, 4' means that 4 is raised to the power of '.
So, to find the value of ', we need to find the value where 4 raised to that power equals 256. We can do this by taking the logarithm base 4 of 256:
log4(256) = '
Using a calculator, we find that the value of ' is 4.
Therefore, it takes 4 hours for the number of bacteria to grow to 2,560. Thus, the answer is c.