# Math

The generation time G for a particular bacterium is the time it takes for the population to double. The bacteria increase in population is shown by the formula G = t over 3.3log a p, where t is the time period of the population increase, a is the number of bacteria at the beginning of the time period, and P is the number of bacteria at the end of the time period. If the generation time for the bacteria is 4.5 hours, how long will it take 4 of these bacteria to multiply into a colony of 7525 bacteria? I understand how to set it up, but I am not getting any of the optional answers as my answer. I don't know how I'd plug it into my calculator.

1. 👍
2. 👎
3. 👁
1. lets find the base a first.

G=4.5=t/(3.3loga(p))
a=4, given in problem
3.3 *4.5log4(p)=t
14.85(log4(7525)=t
but log4(7525)=log10(7525)/log10(4)
14.85*log10(7525)/log10(4)=95.61
t= 95.61 days
<<Change of base formula
Logb x = Loga x/Loga b Pick a new base and the formula says it is equal to the log of the number in the new base divided by the log of the old base in the new base. Solution: Change to base 10 and use your calculator.>>

1. 👍
2. 👎
👤
bobpursley
2. Thank you!! This helps tremendously!

1. 👍
2. 👎
3. 1. B 3/16
2. D 0.3281
3. C 1.31
4. A 95
5. B 43.3013

1. 👍
2. 👎
4. anubis is correct thank you <333

1. 👍
2. 👎

## Similar Questions

1. ### Math

1. Which of the scatter plots above shows a negative trend? A. II B. III C. I D. None of these 2. The scatter plot below shows the population of a village (p) over time (t). Describe the relationship between the population of the

2. ### biochem

Exactly 100 bacteria with a generation time of 30 min are introduced into fresh sterile broth at 8am and maintained at an optimum incubation temperature throughout the day. How many bacterian are present at 3pm? How many

3. ### math

Suppose that the population of a town is described by P=0.16t^2+7.2t+100, where P is the population in thousands and t is the time in years, ( with t=o representing the year 2000). A. what will the population be in 2010? B. what

4. ### Calculus

The rate of growth of a particular population is given by dP/dt=50t^2-100t^3/2 where P is the population size and t is the time in years. The initial population is 25,000. Find the population function. Estimate how many years it

1. ### Pre-Calc

The game commission introduces 100 deer into newly acquired state game lands. the population N of the herd is modeled by N=(20(5+3t))/1+0.04t t>/=0 where t is the time in years a. find the population when t=5, t=10, and t=25 b.

2. ### science

Replication of the E. coli chromosome takes 40 to 45 minutes, but the organism has a generation time of 26 minutes. How does the cell have time to make complete chromosomes for each offspring cell?

3. ### Calculus

The population of a region is growing exponentially. There were 40 million people in 1980 (when t=0) and 50 million people in 1990. Find an exponential model for the population (in millions of people) at any time t, in years after

4. ### Pre Calculus

The population P of a culture of bacteria is described by the equation P = 1600e^0.052t where t is time, in hours, relative to the time at which the population was 1600. (a) What was the population at t = 6 hours? Show your work.

1. ### Math

In 1998, Terre Haute, Indiana had a population of 72,000 people. In 2000, the population had dropped to 70,379. City officials expect the population to level off eventually at 60,000. 1. What kind of function would best model the

2. ### math

The population of a colony of rabbits grows exponentially. The colony begins with 5 rabbits; 5 years later there are 310 rabbits. (a) Express the population of the colony of rabbits, P , as a function of time, t , in years. (b)

3. ### Math - Derivative of a polynomial function(check)

The red squirrel population, p, in a neighborhood park can be modelled by the function p(t)= srqt(210t+44t^2), where t is time in year. a) Determine the rate of growth of the squirrel population at t= 2years Ans: find the 1st

4. ### Calculus

Suppose that you follow the size of a population over time. When you plot the size of the population versus time on a semilog plot (i.e., the horizontal axis, representing time, is on a linear scale, whereas the vertical axis,