1. Assume the pond starts with 500 frogs. For this problem, our unit of population will be a kiloFrog (= 1,000 frogs), so the initial population would be 0.5 kF. Write an equation that represents the number of frogs that will be in the pond next year if we assume that on average there will be two new frogs for each existing frog. No frogs die.

Question

1. Assume the pond starts with 500 frogs. For this problem, our unit of population will be a kiloFrog (= 1,000 frogs), so the initial population would be 0.5 kF. Write an equation that represents the number of frogs that will be in the pond next year if we assume that on average there will be two new frogs for each existing frog. No frogs die.

Answer 1

if there are 2 new frogs, then that means the population has tripled.

After t years, there will be

P(t) = 0.5 * 3^t kF

Answer 2

To write an equation that represents the population of frogs in the pond next year, we will consider the initial population of 0.5 kiloFrogs and the assumption that on average there will be two new frogs for each existing frog.

Let's define the population of frogs in kiloFrogs after "n" years as Pn.

In the first year, the number of new frogs is calculated by multiplying the current population by the average increase of two new frogs per existing frog. So, the new population after one year would be:

P1 = P0 + 2 * P0

Here, P0 represents the initial population of 0.5 kiloFrogs.

Expanding the equation, we get:

P1 = 0.5 + 2 * 0.5

Simplifying further,

P1 = 0.5 + 1 = 1.5 kiloFrogs

Therefore, the equation representing the number of frogs in the pond next year is:

P1 = 1.5 kiloFrogs

This equation can be used to calculate the population of frogs for subsequent years by substituting the previous year's population as Pn-1 in the equation and simplifying to find Pn.