Question

Recal that a variable y satisfies exponential growth it it satistes the diflerental equation y′=k ∗ y (ahere k>0). The solution to this atterential equation is y a c " of (k ∗" t/. where C represents the intial value of y at time f=0. Typically the valus of k is found from innowing the vatue of y at some other tme t. Use this information to selve the following: A bacterit population starts with 4 millon bactera and tiples every 30 minutes. How many bactarla are present anter 45 minutes? Script θ 1 syas k th s DQ NOT CHANGE CODE ON THIS LINE 7 expgra; E Enter the fornuta above as a synbolic expression, replacing C vith the initial value (in aittions). 3) findkinsubs(): s Substitute the tine where y is known a kessolve() h solve (for k ) the equation findk an known y vatue (renenber. to use mi for the equat sign) 3. soln=subs() s substitute the vatues of k and t inte expgr 6 yedouble(soin) s 00 NOT CHANGE COOE oN THIS HTE (Convert to decinal approxination)

Answer 1

To find the number of bacteria after 45 minutes in an exponential growth scenario, we can use the exponential growth equation and substitute the given values. The growth rate constant k can be found by solving the equation using the values of the initial population, time, and the known population at a given time. The number of bacteria present after 45 minutes is approximately 24 million bacteria.

Step-by-step explanation:

To solve this problem, we can use the exponential growth equation

y(t) = y0 * ekt

where y0 is the initial value, t is the time in minutes, and k is the growth rate constant.

1. Given that the bacteria population starts with 4 million bacteria and triples every 30 minutes, we have y0 = 4 million and t = 45 minutes.
2. To find the growth rate constant k, we can use the equation y(t) = y0 * ekt and substitute the values of y0, t, and y(t).
3. Solving for k, we can then substitute the values of k and t into the exponential growth equation to find the number of bacteria present after 45 minutes.

After solving the equations, the number of bacteria present after 45 minutes will be approximately 24 million bacteria.

Learn more about Exponential Growth