We are given a scenario about a cicada apocalypse. The number of cicadas increases by a factor of 1.8 each day. We need to determine the starting value, growth factor, write an equation, and complete a table showing the number of cicadas for the first few days.

1. Problem Description

We are given a scenario about a cicada apocalypse. The number of cicadas increases by a factor of 1.8 each day. We need to determine the starting value, growth factor, write an equation, and complete a table showing the number of cicadas for the first few days.

2. Solution Steps

a) The starting value is the number of cicadas at day

0. From the table, this value is given as 10,

0

0

0.

b) The growth factor is given in the problem as 1.

8. This means the number of cicadas is multiplied by 1.8 each day.

c) The equation is in the form $y = a(b)^x$, where $a$ is the starting value and $b$ is the growth factor. We know that $a = 10000$ and $b = 1.8$. Therefore, the equation is $y = 10000(1.8)^x$.

d) We use the equation $y = 10000(1.8)^x$ to complete the table.

- For day 0: $y = 10000(1.8)^0 = 10000(1) = 10000$

- For day 1: $y = 10000(1.8)^1 = 10000(1.8) = 18000$

- For day 2: $y = 10000(1.8)^2 = 10000(3.24) = 32400$

- For day 3: $y = 10000(1.8)^3 = 10000(5.832) = 58320$

- For day 4: $y = 10000(1.8)^4 = 10000(10.4976) = 104976$

3. Final Answer

a) The starting value is 10,

0

0

0. b) The growth factor is 1.

8. c) The equation is $y = 10000(1.8)^x$.

d) The completed table is:

Day number | Number of Cicadas

---|---

0 (start) | 10,000

1 | 18,000

2 | 32,400

3 | 58,320

4 | 104,976