Answer to Question #159138 in Algebra for Jan

Question

Five hundred yeast cells in a bowl of warm water doubled in number

A every 40 min.

a) Create a graph of the number of yeast cells versus time.

b) Use the graph to determine how long it would take for the total

number of cells to triple (to the nearest minute).

c) Describe how you can adapt your graph to determine the number

of cells for the time before they were monitored.

Answer 1

Five hundred yeast cells in a bowl of warm water doubled in number

A every 40 min.

a) Create a graph of the number of yeast cells versus time.

b) Use the graph to determine how long it would take for the total

number of cells to triple (to the nearest minute).

c) Describe how you can adapt your graph to determine the number

of cells for the time before they were monitored.

Solution

a) The number of yeast cells versus time can be expressed by the formula:

$n=500\cdot2^{\frac{t}{40}}$ , where $t$ - time in min.

b) The total number of cells $=3\cdot500=1500$

$1500=500\cdot2^{\frac{t}{40}}$

$3=2^{\frac{t}{40}}$

$\log_2{3}=\frac{t}{40}$

$t=40\log_2{3}=40\cdot\frac{\log{3}}{\log{2}}=63.3985\approx63$ (min)

c)To determine the number of cells for the time before they were monitored we should substitute the negative values of the time into the formula $n=500\cdot2^{\frac{t}{40}}$ . For example, to determine the number of cells 40 minutes before start monitoring we should substitute t=-40 into the formula $n=500\cdot2^{\frac{t}{40}}=500\cdot2^{-1}=250$ .

Answer:

a)$n=500\cdot2^{\frac{t}{40}}$ ;

b)$t\approx63$ (min);

c)To determine the number of cells for the time before they were monitored we should substitute the negative values of the time into the formula $n=500\cdot2^{\frac{t}{40}}$ .