Doubling and Half-Life

A group of yeast cells doubles every 4 hours. There is a population of 100 cells.

Write an exponential equation to represent the number of yeast cells Y(t), after t hours. 

•  $Y\left(t\right)=100\left(\frac{1}{2}\right)^{\frac{t}{4}}$  

•  $Y\left(t\right)=100\left(2\right)^{4t}$  

•  $Y\left(t\right)=100\left(2\right)^{\frac{t}{4}}$  

•  $Y\left(t\right)=2\left(100\right)^{\frac{t}{4}}$  

A group of yeast cells doubles every 4 hours. There is a population of 100 cells.

How many yeast cells are there after 8 hours. Enter just a number.

A group of yeast cells doubles every 4 hours. There is a population of 100 cells.

What is the percent of growth per hour?

• 1.19%

• 18.9%

• 16%

• 50%

Florine-21 has a half-life of 4 seconds. You begin with a 50 mg sample of Florine-21.

Write an exponential equation to represent the amount of Florine-21, f(t), in mg, after t seconds.

• $f\left(t\right)=50\left(2\right)^{\frac{t}{4}}$

• $f\left(t\right)=50\left(\frac{1}{2}\right)^{4t}$

• $f\left(t\right)=50\left(\frac{1}{2}\right)^{\frac{t}{64}}$

• $f\left(t\right)=50\left(\frac{1}{2}\right)^{\frac{t}{4}}$

Florine-21 has a half-life of 4 seconds. You begin with a 50 mg sample of Florine-21.

How much Florine-21 remains after 15 seconds? Round to the nearest tenth. Enter just a number.

Florine-21 has a half-life of 4 seconds. You begin with a 50 mg sample of Florine-21.

What is the percent of decay per second?

• 15.9%

• 6.25%

• 84.1%

• 65.9%

A certain car loses half of its value every 5 years.

How many years will the computer be worth 12.5% of its initial value?

• 3 years

• 5 years

• 10 years

• 15 years

A certain car loses half of its value every 5 years.

If the value of the car after 8 years is $12,450, what was the initial value of the car?

• $24,900

• $19,920

• $37,741

• $4,107

The number of bacteria on a piece of food on the floor doubles after 10 seconds. The piece of food starts with 45 bacteria on it.

Determine the number of seconds, to the nearest second, will pass until there are 475 cells of bacteria on the piece of food.

Go to desmos.com/calculator to make a table.

In electronics, a capacitor stores electrical energy for future use. As a capacitor is charging, the current across the capacitor decreases exponentially. Suppose that the current across a capacitor decreases from 10 milliamperes (mA) to 2.5 mA in 120 milliseconds(ms) as the capacitor is charging.

What is the half-life of the current in milliseconds?

• 30

• 60

• 120

• 240