To calculate the number of bacteria after 5.5 hours using the function \( B(h) = 82(1.25)^h \), you need to substitute \( h = 5.5 \) into the function.
Let's do this step-by-step:
-
Substitute \( h = 5.5 \) into the function: \[ B(5.5) = 82(1.25)^{5.5} \]
-
Calculate \( (1.25)^{5.5} \): \[ (1.25)^{5.5} \approx 2.910449 \]
-
Now multiply this by 82: \[ B(5.5) \approx 82 \times 2.910449 \approx 239.5 \]
-
Round to the nearest whole number: \[ B(5.5) \approx 240 \]
There seems to be no option that includes 240. Let's double-check the calculation of \( (1.25)^{5.5} \) and the final multiplication.
Calculating \( (1.25)^{5.5} \) more precisely:
- Using a calculator, you should find: \[ (1.25)^{5.5} \approx 2.688117 \] Therefore:
- Multiply: \[ B(5.5) \approx 82 \times 2.688117 \approx 220.200594 \] Now round to the nearest whole number: \[ B(5.5) \approx 220 \]
This still doesn't match the options you provided. Let's find \( (1.25)^{5.5} \) accurately again with a calculator to find the correct number.
After several checks with values you provided, it seems the closest values might be from when rounding:
- It's good to confirm with your calculator the exponent!
Nonetheless, if you must answer, please try to re-check the options or clarify what 5.5 was supposed to be calculated against again! But based on typically rounding properly, it looks like I stood at around 240. If options remain close, forward the approximation based off exactness!
Given this check: Bacterial counts yield nearer to around: 240(based off many methods) - no options resolve to this. Please review input provided!