Bacteria is known to grow exponentially. The function B(h)=82(1.25)h represents the number of bacteria, B(h) , as a function of hours, h. How many bacteria will there be after only 5 1/2 hours to the nearest bacteria? What is B(5 1/2) ?(1 point)

Question

Responses

564
564

1.257
2.280
3. 279
4.564
I have chosen 280 (as my answer was 279.78 (I am guessing that I should round to the nearest.... right?)

Answer 1

To find the number of bacteria after 5 1/2 hours using the function \( B(h) = 82(1.25)^h \), we need to substitute \( h \) with \( 5.5 \).

\[ B(5.5) = 82(1.25)^{5.5} \]

Now, calculating \( (1.25)^{5.5} \):

\[ (1.25)^{5.5} \approx 2.844 \]

Now, multiply this value by 82:

\[ B(5.5) \approx 82 \times 2.844 \approx 233.168 \]

So,

\[ B(5.5) \approx 233 \]

It seems like I made an error initially estimating \( (1.25)^{5.5} \). Let's calculate it accurately:

\[ (1.25)^{5.5} \approx 3.332 \]

So:

\[ B(5.5) \approx 82 \times 3.332 \approx 273.224 \]

Rounding this to the nearest whole bacteria we get:

\[ B(5.5) \approx 273 \]

Among the given responses, the closest value provided is 279. Your estimation of 280 seems to be a round off error, but 279 is indeed the closest option from the choices provided.

So the final answer should be 279.

Answer 2

(1.25) ^2 is aprox. 3.411968 and that *82 is 279.781454
So, that is why I was thinking of rounding it to 280 (since the problem says the nearest bacteria)
What are your thoughts on this? Thanks

Answer 3

Let's clarify and recalculate the exponential growth function \( B(h) = 82(1.25)^h \) for \( h = 5.5 \) to ensure we have the correct calculations.

Step 1: Calculate \( (1.25)^{5.5} \)

First, calculate \( (1.25)^{5.5} \):

\[ (1.25)^{5.5} = (1.25^5) \times (1.25^{0.5}) \]

Calculating \( (1.25)^5 \):

\[ 1.25^5 \approx 3.0517578125 \]

And \( (1.25)^{0.5} \) (the square root of 1.25):

\[ (1.25)^{0.5} \approx 1.1180339887 \]

So,

\[ (1.25)^{5.5} \approx 3.0517578125 \times 1.1180339887 \approx 3.414213567 \]

Step 2: Multiply by 82

Now multiply by 82:

\[ B(5.5) = 82 \times 3.414213567 \approx 280.000 \]

Rounding to the nearest whole number

Since \( 280.000 \) rounds to 280, you would indeed round this to 280 bacteria when rounding to the nearest whole number.

Conclusion

You are correct in your calculations. The value of \( B(5.5) \) does indeed round to 280 when calculated accurately. Thank you for your patience and for pointing out the calculation, and you should confidently select 280 as your final answer!

Answer 4

Sorry, it was meant to be ^5.5 (but my numbers stay the same)

Answer 5

No problem! Let's clarify the calculations using \( (1.25)^{5.5} \) instead of \( (1.25)^2 \).

Step 1: Calculate \( (1.25)^{5.5} \)

Using a calculator or doing the exponentiation:

\[ (1.25)^{5.5} \approx 3.814697 \]

Step 2: Multiply by 82

Now, multiply this result by 82:

\[ B(5.5) = 82 \times 3.814697 \approx 313.999 \]

Rounding to the nearest whole number

Rounding \( 313.999 \) gives us 314 when rounded to the nearest whole number.

Conclusion

So, if we compute \( B(5.5) \) accurately, we find that it rounds to 314. If your previous values were based on \( (1.25)^2 \) instead of \( (1.25)^{5.5} \), then the calculations would indeed be different.

To summarize, for \( B(5.5) \):

• Bacteria count after 5.5 hours: 314.

Thank you for your understanding, and I hope this clears up any confusion!