applications of exponential functions!

[ergim142]

-) The handling of ground beef must be carefully monitored to ensure that people do not ingest E. coli bacteria.Suppose a particular package of ground beef has 5 E. coli bacteria per square centimetres.After being left on the counter for 30 mins. , the package had 20 bacteria per square centimetre.Assume the E coli grows exponentially.
A) Determine the equation that describes the concentration.C,of E coli bacteria in terms of time , t, in minutes.
B) What will be the concentration of E coli bacteria 100 minutes after the package is left out on the counter?
C) If the mathematical model only applies for the first four hours,state the domain and range of the function.
Domain=?
Range=?

 

[skeeter]

-) The handling of ground beef must be carefully monitored to ensure that people do not ingest E. coli bacteria.Suppose a particular package of ground beef has 5 E. coli bacteria per square centimetres.After being left on the counter for 30 mins. , the package had 20 bacteria per square centimetre.Assume the E coli grows exponentially.
A) Determine the equation that describes the concentration.C,of E coli bacteria in terms of time , t, in minutes.
B) What will be the concentration of E coli bacteria 100 minutes after the package is left out on the counter?
C) If the mathematical model only applies for the first four hours,state the domain and range of the function.
Domain=?
Range=?

ordered pairs ... \(\displaystyle (t,y)\) where t is time in minutes and y is the number of bacteria per \(\displaystyle cm^2\)

you have two ordered pairs from the problem statement ... (0,5) and (30,20)

natural exponential growth model is \(\displaystyle y(t) = y(0) \cdot e^{kt}\)

use the two ordered pairs to determine \(\displaystyle y(0)\) and the growth constant k

domain is \(\displaystyle 0 \le t \le 4\) , so the range is \(\displaystyle y_0 \le y \le y(4)\)