Question

dr. jimenez found that after applying an antibiotic to bacteria, he observed only 90% of the bacteria left in the culture dish each hour. if the initial bacteria count was 100, what was the bacteria count after 5 hours? round to the nearest whole number.

there were \boxed{} bacteria after 5 hours.

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $N(t) = N_0 \times r^t$, where $N_0$ is the initial amount, $r$ is the rate of decay (as a decimal), and $t$ is the time. Here, $N_0 = 100$, $r = 0.9$ (since 90% left means 0.9 of the previous amount remains), and $t = 5$.

Step2: Substitute the values into the formula

Substitute $N_0 = 100$, $r = 0.9$, and $t = 5$ into the formula: $N(5) = 100 \times (0.9)^5$.

Step3: Calculate $(0.9)^5$

First, calculate $(0.9)^5 = 0.9 \times 0.9 \times 0.9 \times 0.9 \times 0.9 = 0.59049$.

Step4: Multiply by the initial amount

Multiply 100 by 0.59049: $100 \times 0.59049 = 59.049$.

Step5: Round to the nearest whole number

Rounding 59.049 to the nearest whole number gives 59.

Answer:

59