Your baby brother has an ear infection. The doctor said they’re about 50000000 bacteria in his left ear. The penicillin the doctor prescribed, will kill 7% of the bacteria every hour how many bacteria will be in your brothers year and a day from your answer to the nearest whole number

Answer 1

To find out how many bacteria will remain in your baby brother's ear after one day (24 hours) given that 7% of the bacteria are killed every hour, we can follow these steps:

1. Start with the initial number of bacteria: 50,000,000.
2. Calculate the percentage of bacteria that remain after each hour. If 7% are killed, then 93% remain, which can be expressed as a decimal:
   \[ 93% = 0.93 \]
3. The number of bacteria remaining after one hour can be calculated as:
   \[ \text{Remaining bacteria after 1 hour} = 50,000,000 \times 0.93 \]
4. For 24 hours, we need to raise the remaining percentage (0.93) to the power of the number of hours (24): \[ \text{Remaining bacteria after 24 hours} = 50,000,000 \times (0.93)^{24} \]

Now let's calculate it step by step:

1. Calculate \( (0.93)^{24} \): \[ (0.93)^{24} \approx 0.509 \] (This value can be calculated using a calculator).

2. Now we can find the remaining bacteria after 24 hours: \[ \text{Remaining bacteria} = 50,000,000 \times 0.509 \approx 25,450,000 \]

Rounding to the nearest whole number, the number of bacteria remaining after one day in your brother's ear would be:
25,450,000.

Answer 2

In a week

Answer 3

To find out how many bacteria will remain in your baby brother's ear after one week (7 days or 168 hours), we can use the same approach as before.

1. Start with the initial number of bacteria: 50,000,000.
2. After each hour, 93% of the bacteria remain. We need to find out how much remains after 168 hours.
3. We can calculate the remaining bacteria after 168 hours using the formula: \[ \text{Remaining bacteria} = 50,000,000 \times (0.93)^{168} \]

Now, let's calculate \( (0.93)^{168} \):

1. Calculate \( (0.93)^{168} \): \[ (0.93)^{168} \approx 0.00028 \text{ (using a calculator)} \]

2. Now substitute back into the equation: \[ \text{Remaining bacteria} = 50,000,000 \times 0.00028 \approx 14,000 \]

Rounding to the nearest whole number, the number of bacteria remaining after one week would be approximately:
14,000 bacteria.

Answer 4

3 hours

Answer 5

To find out how many bacteria will remain in your baby brother's ear after 3 hours, we'll go through the calculations step by step using the same approach.

1. Initial number of bacteria: 50,000,000

2. Percentage of bacteria remaining after each hour: 93% (or 0.93 as a decimal)

3. Calculate the remaining bacteria after 3 hours using the formula:

   \[ \text{Remaining bacteria} = 50,000,000 \times (0.93)^{3} \]

Now, let's calculate it:

1. Calculate \( (0.93)^{3} \): \[ (0.93)^{3} \approx 0.804357 \]

2. Now substitute back into the equation: \[ \text{Remaining bacteria} = 50,000,000 \times 0.804357 \approx 40,217,850 \]

Rounding to the nearest whole number, the number of bacteria remaining after 3 hours would be approximately:
40,217,850 bacteria.