It is important to recognize that this is an exponential rate of increase. If the population doubles every 3 days, then using x as the number of people who would be infected today, you can trace the growth exponentially using:

Today: x people

3 days from now: 2x people

6 days from now: 4x people (2x will have doubled to 4x)

9 days from now: 8x people (4x will have doubled to 8x)

So the correct ratio is 1:8.

A decrease of is the same thing as a decrease of , since , which reduces to . A convenient way to handle percent decreases is to think that if has been taken away, then is left. So you can multiply by to get .

We can set up equations for income before and after the wage reduction. Initially, the employee earns wage and works hours per week. After the reduction, the employee earns wage and works hours. By setting these equations equal to each other, we can determine the increase in hours worked: (divide both sides by ) We know that the new number of hours worked will be 25% greater than the original number.

Whenever you're provided an equation for how to calculate an exponential outcome from an exponential proportion, it's helpful to try to solve the problem algebraically, as often the results are not directly intuitive to try to solve just conceptually. Here you're given the current population, , and the way that that population can be calculated based on the number of days, . You can then set the population equal to and perform the algebra:

You can divide both sides by to simplify:

And then take the square root of both sides:

Multiply both sides by 2 and you have the answer,

We can use dimensional analysis to solve this problem. We will create ratios from the conversions given.

Since Joaquin cannot trade for part of a shiny rock, the most he can get is shiny rocks.

Whenever you're provided an equation for how to calculate an exponential outcome from an exponential proportion, it's helpful to try to solve the problem algebraically, as often the results are not directly intuitive to try to solve just conceptually. Here you're given the current population, , and the way that that population can be calculated based on the number of days, . You can then set the population equal to and perform the algebra:

You can divide both sides by to simplify:

And then take the square root of both sides:

Multiply both sides by 2 and you have the answer,

It is important to recognize that this is an exponential rate of increase. If the population doubles every 3 days, then using x as the number of people who would be infected today, you can trace the growth exponentially using:

Today: x people

3 days from now: 2x people

6 days from now: 4x people (2x will have doubled to 4x)

9 days from now: 8x people (4x will have doubled to 8x)

So the correct ratio is 1:8.

A decrease of is the same thing as a decrease of , since , which reduces to . A convenient way to handle percent decreases is to think that if has been taken away, then is left. So you can multiply by to get .

We can use dimensional analysis to solve this problem. We will create ratios from the conversions given.

Since Joaquin cannot trade for part of a shiny rock, the most he can get is shiny rocks.

We can set up equations for income before and after the wage reduction. Initially, the employee earns wage and works hours per week. After the reduction, the employee earns wage and works hours. By setting these equations equal to each other, we can determine the increase in hours worked: (divide both sides by ) We know that the new number of hours worked will be 25% greater than the original number.