Question

Marco starts with a population of 10 bacteria that doubles every day for a number of days, d. He writes the expression 10(2d) to find the number of bacteria after d days. Isabella starts with a population of 1 bacterium that increases 20% every day for a number of days, d. She writes the expression (1 + 0.2)d to find the number of bacteria after d days. Use the drop-down menus to explain what each part of Marco's and Isabella's expressions mean.

Answer 1

Explanation:

Answer 2

Marco- 10 is the starting value of the population. 2 is the growth rate of "double each day" with d as an exponent.

Isabella- 1 is the starting population. 1+0.2=1.2 is the rate at which it grows each day.

Explanation:

Marco's equation should be
`10(2^(d))` since the bacteria double each day. 10 is the starting value of the population. 2 is the growth rate of "double each day" with d as an exponent. This will double each day because:

Day 1 is
`2^(1)=2`

Day 2 is
`2^(2)=4`

Day 3 is
`2^(3)=8`

Day 4 is
`2^(4)=16`

You'll notice the value doubles each day.

Isabella has a different equation because her population increases by a percentage. We use the simple interest formula to calculate the bacteria's daily increase or interest.

1(1+0.2)d

1 is the starting population.

1+0.2=1.2 is the rate at which it grows each day.