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1 month ago
12

Harriet is cultivating a strain of bacteria in a petri dish. Currently, she has 103 bacteria in the dish. The bacteria divide ev

ery two hours such that the number of bacteria has doubled by the end of every second hour. How many bacteria will Harriet have in the dish at the end of 6 hours
Mathematics
2 answers:
zzz [11K]1 month ago
8 0
According to the stated conditions, the quantity of bacteria at any time t (in hours) can be determined using the following equation,
                                         at = (a1)(2^t/2)

where a1 denotes the initial bacteria count and at represents the count at time t. By using the provided numbers,
                                      a6 = (103)(2^6/2) = 824 

Consequently, there are 824 bacteria present after 6 hours. 
Inessa [11.2K]1 month ago
6 0

Formula for growth or decay

R= R_{0}[1 \pm \frac{r}{100}]^t

R= Population of bacteria at the end

R_{0}= Initial population

r = Growth or decay rate

t= Duration

R_{0}= 103 bacteria

for t=2

R equates to 103 × 2= 206 bacteria

By substituting these values into the growth formula

206 = 103 × (1+ \frac{r}{100})^2

When we divide both sides by 103, we arrive at

2 = (1+ \frac{r}{100})^2

(1+ \frac{r}{100})= √2------(1)

(1+ \frac{r}{100})= 1.414

r = (1.414 -1) × 100=.414 × 100= 41.4%

At the end of 6 hours, the bacteria count will be = 103 × (1+ \frac{r}{100})^6= 103 × [\sqrt{2}]^6 ------Utilizing (1)

= 103 × 2³

= 103 × 8

= 824→→the quantity of bacteria that Harriet will have in the dish after 6 hours


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