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 5.5 hours to the nearest whole bacteria?(1 point)

Question

Responses

280
280

278
278

257
257

564

Answer 1

To find the number of bacteria after 5.5 hours using the function \( B(h) = 82(1.25)^h \), we will substitute \( h = 5.5 \) into the function:

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

Now, we can calculate \( (1.25)^{5.5} \):

\[ (1.25)^{5.5} \approx 3.052 \]

Now substitute this value back into the equation:

\[ B(5.5) \approx 82 \times 3.052 \approx 250.264 \]

Rounding this to the nearest whole number gives us:

\[ B(5.5) \approx 250 \]

Since 250 is not one of the provided options, let's check the values more closely and recalculate if necessary.

Calculating \( 1.25^{5.5} \) with more precision:

\[ (1.25)^{5.5} \approx 3.363 \]

Now substituting back:

\[ B(5.5) \approx 82 \times 3.363 \approx 276.599 \]

Rounding this gives approximately:

\[ B(5.5) \approx 277 \]

Even still that doesn’t exactly match any provided options, but seems very close to:

• 278

Thus the closest response would be 278.