Question
Bacteria are known to grow exponentially. The function B(h)=82(1.25)^h represents the number of bacteria, B(h), as a function of h. How many bacteria will there be after only 5.5 hours, to the nearest whole number?
280
257
564
280
257
564
Answers
GPT-4o mini
To find the number of bacteria after 5.5 hours using the function \( B(h) = 82(1.25)^h \), we need to evaluate \( B(5.5) \):
\[
B(5.5) = 82(1.25)^{5.5}
\]
First, we calculate \( (1.25)^{5.5} \):
\[
(1.25)^{5.5} \approx 2.44140625
\]
Now we substitute this value back into the equation:
\[
B(5.5) = 82 \times 2.44140625 \approx 200.0
\]
Now we perform the multiplication:
\[
B(5.5) \approx 82 \times 2.44140625 \approx 200.0
\]
Calculating this precisely gives us:
\[
B(5.5) = 82 \times (1.25)^{5.5} \approx 82 \times 2.44140625 \approx 200.0
\]
Finally, rounding 200 to the nearest whole number gives:
\[
B(5.5) \approx 200
\]
From the options provided, none of them match this calculation directly. Please verify if there is any rounding or mathematical operation that was not considered. But the calculation indicated gives roughly 200 bacteria after 5.5 hours.
If you want a more refined calculation or interpretation, please do let us know!
\[
B(5.5) = 82(1.25)^{5.5}
\]
First, we calculate \( (1.25)^{5.5} \):
\[
(1.25)^{5.5} \approx 2.44140625
\]
Now we substitute this value back into the equation:
\[
B(5.5) = 82 \times 2.44140625 \approx 200.0
\]
Now we perform the multiplication:
\[
B(5.5) \approx 82 \times 2.44140625 \approx 200.0
\]
Calculating this precisely gives us:
\[
B(5.5) = 82 \times (1.25)^{5.5} \approx 82 \times 2.44140625 \approx 200.0
\]
Finally, rounding 200 to the nearest whole number gives:
\[
B(5.5) \approx 200
\]
From the options provided, none of them match this calculation directly. Please verify if there is any rounding or mathematical operation that was not considered. But the calculation indicated gives roughly 200 bacteria after 5.5 hours.
If you want a more refined calculation or interpretation, please do let us know!