If the number of bacteria in a colony doubles every 210 minutes and the population is currently 8,000 bacteria, what will the population be in 630 minutes and is it modeled by a linear function or a exponential function? A) 24,000; linear function B) 24,000; exponential function C) 64,000; linear function D) 64,000; exponential function

Accepted Solution

Answer:Option D. 64000 ; exponential function.Step-by-step explanation:Since number of bacteria in a colony doubles every 210 minutes.Therefore the function will be modeled by an exponential function with a common ratio of 2.Currently the population is 8000 bacteria.Therefore the expression will be [tex]T_{n}=ar^{nk}[/tex]Here a = initial populationn = time or periodTn = population after n minutesk = constant[tex]T_{210}=8000(2)^{210(k)}=16000[/tex][tex]2^{210k}=2^{1}[/tex]210k = 1 β‡’ [tex]k=\frac{1}{210}[/tex]Now we have to find the population after 630 minutes.[tex]T_{n}=ar^{nk}[/tex][tex]T_{630}=8000(2)^{\frac{630}{210}}=8000(2)^{3}=64000[/tex]Therefore the answer is option D). 64000 ; exponential function.