Question

2. A culture of bacteria doubles every two hours. If there are 500 bacteria at the

beginning, how many bacteria will there be after 24 hours? (Geometric series)​

Answer 1

Answer:

ANSWER:  2,048,000

Step-by-step explanation:

Clue for common ratio: "doubles"

Therefore common ratio (r) = 2

Clue for which term (n) is after 24 hours: "every two hours... for 24 hours".

Therefore "after" 24 hours n = (24 ÷ 2) + 1

                                          n = 12 + 1

                                          n = 13

an = a₁  

a₁ = 500          r = 2          n = 12        an/a₁₃ = ?

a₁₃ = 500 (2)¹³ ⁻ ¹

a₁₃ = 500 (2)¹²

a₁₃ = 500 (4,096)

a₁₃ = 2,048,00

ANSWER:  2,048,000

PLZ MARK AS BRAINLIEST

Answer 2

Given,

Initial bacteria, $\[a = 500\]$

Bacteria doubles after every 2 hours.

Solution,

$\[\begin{array}{l}a = 500\\r = 2hours\\n = \frac{{24}}{2} + 1\\ \Rightarrow n = 13\end{array}\]$

Calculate the bacteria after 24 hours,

$\[\begin{array}{l}{a_{13}} = a{r^{n - 1}}\\ \Rightarrow {a_{13}} = 500 \times {2^{13 - 1}}\\ \Rightarrow {a_{13}} = 500 \times {2^{12}}\\ \Rightarrow {a_{13}} = 2048000\end{array}\]$

Hence the number of bacteria after 24 hours is $\[2048000\]$