Question

determine the population after the given number of hours by substituting the known values for the variables in the exponential growth formula and simplifying. the initial cell population, c, of 2,000 is given and the growth constant, k, was found to be approximately 0.55962. find the population, y, when t = 4 hours. substitute these values into the exponential growth formula. simplify the right side of the equation using a calculator with an e button. (round your answer to the nearest whole number.) y = ce^{kt} = 2,000e^{0.55962(4)} = 9.37803 × therefore, rounded to the nearest whole number, after 4 hours the bacteria culture will have about how many cells? 18756.06 × cells

Explanation:

Step1: Calculate the exponent

First, calculate the value of the exponent \(0.55962\times4 = 2.23848\).

Step2: Calculate the exponential part

Then, find the value of \(e^{2.23848}\). Using a calculator, \(e^{2.23848}\approx9.37803\).

Step3: Calculate the final population

Now, multiply the initial population \(C = 2000\) by the value of \(e^{kt}\). So, \(y=2000\times9.37803\).

$$y = 2000\times9.37803=18756.06\approx18756$$

Answer:

\(18756\)