So for this question: The number of bacteria present in a culture is given by the following model B=1000e^0.276t; where t= time in minutes. Find the time required to have 6000 bacteria present. Then, round your answer to the nearest tenth of a minute; would my answer be 6.5?

Apparently so, since that is what you provide.

My answer is arrived at in this wise:

1000e^0.276t = 6000
e^0.276t = 6
0.276t = ln6
t = ln6/0.276
t = 6.49188

So, 6.5 is the correct answer. Good job.

To find the time required to have 6000 bacteria present, we can substitute B = 6000 into the given model:

6000 = 1000*e^(0.276t)

Now, divide both sides of the equation by 1000:

6 = e^(0.276t)

To isolate the exponential term, take the natural logarithm (ln) of both sides:

ln(6) = ln(e^(0.276t))

Using the logarithmic property ln(e^x) = x:

ln(6) = 0.276t

Now, divide both sides by 0.276:

t = ln(6)/0.276

Using a calculator, we find:

t ≈ 5.59 minutes

Rounding to the nearest tenth of a minute, the time required to have 6000 bacteria present is approximately 5.6 minutes, not 6.5 minutes.

To find the time required to have 6000 bacteria present in the culture, we need to solve the equation B = 6000, where B represents the number of bacteria and t represents the time in minutes.

The given model is B = 1000e^(0.276t). Setting B equal to 6000, we have:

6000 = 1000e^(0.276t)

To solve for t, we first divide both sides by 1000:

6 = e^(0.276t)

Next, we take the natural logarithm (ln) of both sides to isolate the exponent:

ln(6) = ln(e^(0.276t))

Using the property of logarithms that ln(e^x) = x, we get:

ln(6) = 0.276t

Finally, to solve for t, we divide both sides by 0.276:

t = ln(6) / 0.276

Using a calculator or math software, we can calculate this value. Rounding to the nearest tenth of a minute, the time required to have 6000 bacteria present is approximately 6.6 minutes, not 6.5 minutes.