Chapter 8.2, Problem 5CYU

(a)

To determine

To find: the exponential function for the given condition.

Answer to Problem 5CYU

The exponential function for the given condition is $C=2^{\frac{t}{15}}$ .

Explanation of Solution

Given information:

The given condition is given by “ The Escherichia coli can reproduce itself in 15 minutes”.

If the base of any two exponential functions are equal then the exponent of the function are also equal. If $a^x=a^y$ then $x=y$ .

Consider the given condition.

The Escherichia coli can reproduce itself in 15 minutes.

The exponential function that represents the number of cells after $t$ minutes can be written as $C=2^{\frac{t}{x}}$ .

Substitute 15 for $x$ in the function $C=2^{\frac{t}{x}}$ to find the exponential function.

  $C=2^{\frac{t}{15}}$

Therefore, the exponential function for the given condition is $C=2^{\frac{t}{15}}$ .

(b)

To determine

To find: the number of cells will be in one hour.

Answer to Problem 5CYU

The number of cells of bacteria will be in one hour is $16$ .

Explanation of Solution

Given information:

The given condition is given by “The Escherichia coli can reproduce itself in 15 minutes”.

If the base of any two exponential functions are equal then the exponent of the function are also equal. If $a^x=a^y$ then $x=y$ .

Consider the given condition.

The Escherichia coli can reproduce itself in 15 minutes.

Consider the given condition.

  $C=2^{\frac{t}{15}}$

Substitute $60$ for $x$ in the function $C=2^{\frac{t}{15}}$ to find the exponential function.

  $\begin{array}{c}C=2^{\frac{t}{15}}\\ =2^{\frac{60}{15}}\\ =2^4\\ =16\end{array}$

Therefore, the number of cells of bacteria will be in one hour is $16$ .