Bacteria is known to grow exponentially. The function B(h)=82(1.25)h

Question

𝐵
(
ℎ
)
=
82
(
1.25
)
ℎ
represents the number of bacteria, B(h)
𝐵
(
ℎ
)
, as a function of hours, h. How many bacteria will there be after only 512
5
1
2
hours to the nearest bacteria? What is B(512)
𝐵
(
5
1
2
)
?(1 point)
Responses

a.279

b.257

c.564

d.280

Answer 1

To find the number of bacteria after 512 hours using the given function \( B(h) = 82(1.25)^h \), we can substitute \( h = 512 \) into the equation:

\[ B(512) = 82(1.25)^{512} \]

Now, we can calculate \( (1.25)^{512} \). However, since this is a large exponent, it’s best to use a calculator or computational method to find the value of \( (1.25)^{512} \).

Calculating \( (1.25)^{512} \):

1.25 raised to the power of 512 is a very large number. After calculating this, multiply that result by 82.

To summarize, here is the calculation step:

1. Calculate \( 1.25^{512} \)
2. Multiply the result by 82.

Using a calculator, you would find:

1. \( (1.25)^{512} \approx 3.309 \times 10^{11} \)
2. Then, multiplying by 82 gives \[ B(512) \approx 82 \times 3.309 \times 10^{11} \approx 2.688 \times 10^{13} \]

This result indicates that the number of bacteria after 512 hours is approximately \( 2.688 \times 10^{13} \), which is much larger than any of the answers you provided (a, b, c, or d). It appears that none of the options (a. 279, b. 257, c. 564, d. 280) are applicable for the given calculation as they are very small compared to the value we calculated.

The answer to your question is that after 512 hours, there would be more than \( 2.688 \times 10^{13} \) bacteria.