Question

Please help me with this.

Answer 1

The rate of change would be 300 bacteria per minute at 0.1 minutes past 1 PM

The exponential function of the bacteria

The given parameters are:

Initial, a = 20

At 30 minutes, Value = 500

An exponential function is represented as:

y = ab^t

Where a is the initial value.

So, we have:

y = 20b^t

After 30 minutes, we have:

20b^30 = 500

Divide both sides by 20

b^30 = 25

Take the 30th root of both sides

b = 1.11

Substitute b = 1.11 in y = 20b^t

y = 20(1.11)^t

Hence, the exponential model is y = 20(1.11)^t

Minutes to reach 11,000

This means that:

y = 11,000

So, we have:

20(1.11)^t = 11000

Divide both sides by 20

1.11^t = 550

Take the logarithm of both sides

tlog(1.1) = log(550)

Divide both sides by log(1.1)

t = 66

Hence, the population would reach 11,000 after 66 minutes

The population at 2PM

This means that:

t = 60 i.e. 60 minutes after 1PM

So, we have:

y = 20(1.11)^60

Evaluate

y = 10481

Hence, the population at 2PM is 10481

The rate of change at 2PM

In (c), we have:

y = 10481 ------ population at 2PM is 10481

t = 60

The rate of change is calculated as:

Rate = 10481/60

Evaluate

Rate = 174.68

Hence, the rate of change at 2PM is 174.68 bacteria per minute.

When the rate would be 300 bacteria per minute?

The rate of change is calculated as:

Rate = Population/Time

So, we have:

y/t = 300

This gives

y = 300t

Substitute y = 300t in y = 20(1.11)^t

300t = 20(1.11)^t

Divide both sides by 20

15t = (1.11)^t

Using a graphing calculator, we have:

t = 0.1

Hence, the rate would be 300 bacteria per minute at 0.1 minutes past 1 PM

Read more about exponential functions at:

brainly.com/question/11464095

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