MATH SOLVE

3 months ago

Q:
# (40pts) Help pleasebacteria are the most common example of exponential growth The table below shows the number of E-coli bacteria that would be present after each hour of the first six hours.

Accepted Solution

A:

Answer: a) each hour the number is multiplied by 16. Such a geometric sequence is described by an exponential growth function. b) n = 16^t . . . . . n is number of bacteria; t is hours c) about 7.923Γ10^28 d) the rule would be multiplied by 100/16=6.25, so becomes n=6.25Β·16^tStep-by-step explanation:a) We presume the table represents exponential growth because it was formulated with that purpose in mind. ("Why?" is always a tricky question.) It represents exponential growth because each table entry is 16 times the one before. A constant multiplier like that is characteristic of exponential growth.___b) In part (a) we noted the common ratio is 16. Since the first term (for t=1) is also 16, we can write the equation as ... n = 16^twhere n is the number of bacteria and t is time in hours___c) Evaluating the formula for t=24, we get ... n = 16^24 β 7.923Γ10^28 n = 79,228,162,514,264,337,593,543,950,336This is the estimate of the number present after 24 hours based on the formula.___d) If the starting number is different, the rule is multiplied by a factor that gives the appropriate starting value. The above answer assumes your "starting value" is 100 after 1 hour. If the starting value at 0 hours is 100, then the rule of part (b) gets multiplied by 100, not 6.25 n = 100Β·16^t . . . . . starting with 100 at t=0 n = 6.25Β·16^t . . . . starting with 100 at t=1_____Comment on exponential bacteria growthThe number of bacteria estimated in part (c) have an approximate volume of 102 cubic kilometers, roughly the volume of Lake Nicaragua.