(a)

The function is , where represents the time and measured in days.

Graph :

Draw a coordinate plane.

Plot the data.

Graph the function   for :.

(b)

The function is .

Substitute in above function.

The number of bacteria when is .

(c)

Observe the graph of the function .

The number of bacteria reaches its maximum early on the seventh day.

(d)

Draw a coordinate plane.

Use a graphing utility first graph the function .

Then graph the .

After then graph the function .

Graph :

Observe the above graph :

The function is greatest when .

This is the inflection point.

Therefore, the rate increase in the number of bacteria is greatest in the early part of the thord day.

(e)

Find.

Therefore, .

(a)

Graph of the function   for :

(b)

The number of bacteria when is .

(c)

The number of bacteria reaches its maximum early on the seventh day.

(d)

The rate increase in the number of bacteria is greatest in the early part of the thord day.

(e)

.