# Calculus

posted by .

A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. At the end of 2 hours, there are 4,800 bacteria. At the end of 4 hours, there are 19,00 bacteria. How many bacteria were present initially?

• Calculus -

A = P*e^kt

4800 = P*e^2k
19000 = p*e^4k

Now, 4800/p = e^2k, so
19000 = p*(4800/p)^2
19000 = 4800^2/p
p = 4800^2/19000 = 1212

just for grins, what's k?

4800=1212*e^2k
e^2k = 3.958
2k = ln 3.958 = 1.376
k = 0.688

so, A(x) = 1212*e^.688t

• Calculus -

Bacteria experiment. If after one hour there were 1600 bacteria. Three hours later there was 400 bacteria. How many bacteria were there originally?

## Similar Questions

1. ### calculus

a bacteria pop. grows exponentially. There are 1500 bacteria after 3 hours and 20,000 after 8 hours. ahving trouble finding the initial bacteria pop. thanks for the help In five hours the population get's larger by a factor 13 + 1/3-----> …
2. ### Calculus

Suppose that a population of bacteria triples every hour and starts with 700 bacteria. (a) Find an expression for the number n of bacteria after t hours. n(t) = ?
3. ### Pre-Calc (exponential growth)

A COLONY OF BACTERIA IS GROWN UNDER IDEAL CONDITIONS IN A LAB SO THAT THE POPULATION INCREASES EXPONENTIALLY WITH TIME. At the end of the three hours, there are 10,000 bacteria. At the end of the 5 hours, there are 40,000 bacteria. …
4. ### Calc

The number of bacteria in a culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours. a) Find the initial population. b) Write an exponential …
5. ### Math- Alg 2

A colony of bacteria is growing exponentially according to the function below, where T is in hours. How many bacteria are there after 7 hours?
6. ### Pre Cal

A certain strain of bacteria divides every four hours. If a colony is started with 10 bacteria, then the time t (in hours) required for the colony to grow to N bacteria is given by t = 4(log(N/10)/log2 Find the time required for the …
7. ### Calculus

Under a set of controlled laboratory conditions, the size of the population of a certain bacteria culture at time t (in minutes) is described by the following function. P = f(t) = 3t^2 + 2t + 1 Find the rate of population growth at …
8. ### Calculus

The population of a colony of bacteria is modeled by the function p(x)=50(e^-x - e^-x^2)+10 ,for 0 ≤ x, where population P is in thousands, x is in hours, and x = 0 corresponds to the moment of introduction of a certain chemical …
9. ### Algebra

Under ideal conditions, a population of e. coli bacteria can double every 20 minutes. This behavior can be modeled by the exponential function: N(t)=N(lower case 0)(2^0.05t) If the initial number of e. coli bacteria is 5, how many …
10. ### pre calc

The number N of bacteria in a culture at time t (in hours) grows exponentially according to the function N(t) = 1000e^0.01t. 1.What is the population after 4 hours?

More Similar Questions