Question

2
there are 2,700 bacteria in a lab dish. the number of bacteria decreases 8% per day. compare the decrease in number of bacteria for days 1 to 3 to the decrease for days 4 to 6.

the number of bacteria decreases ____ from day 1 to day 3 than from day 4 to day 6.
options:
equal
slower
faster

Explanation:

Step1: Define decay formula

The number of bacteria after $t$ days follows the exponential decay model:
$N(t) = N_0(1-r)^t$
where $N_0=2700$, $r=0.08$

Step2: Calculate bacteria at day 0,3,6

• $N(0) = 2700(1-0.08)^0 = 2700$
• $N(3) = 2700(0.92)^3 = 2700 \times 0.778688 = 2102.4576$
• $N(6) = 2700(0.92)^6 = 2700 \times 0.606355 = 1637.1585$

Step3: Find total decrease (days1-3)

Decrease = $N(0) - N(3)$
$= 2700 - 2102.4576 = 597.5424$

Step4: Find total decrease (days4-6)

Decrease = $N(3) - N(6)$
$= 2102.4576 - 1637.1585 = 465.2991$

Step5: Compare the two decreases

$597.5424 > 465.2991$, so the decrease is faster in days1-3.

Answer:

faster