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The steps in the patterns A and B form a sequence
The attached diagram represents dots in patterns A and B
<h3>How to draw the diagrams</h3>For pattern A, we have:
Step 2 = 10 dots
Increment of 3 dots in each step
This means that:
Step 0 = 4 dots
Step 1 = 7 dots
Step 2 = 10 dots
Step 3 = 13 dots
For pattern A, we have the following rule
When n = 0 to 3, we have:
Step 0 = 1 dot
Step 1 = 3 dots
Step 2 = 9 dots
Step 3 = 19 dots
Next, we draw the diagrams of both patterns (see attachment)
Read more about patterns at:
Answer:
a)
The initial amount is 141,200.
The decay factor is 0.89, and the decay rate is of 0.11 = 11%.
b)
The function is
The number of bats in 2003 was of 13,729.
Step-by-step explanation:
Exponential decay function:
An exponential decay function has the following format:
In which y(0) is the initial value, 1 - r is the decay factor and r is the decay rate, as a decimal.
A. Identify the initial amount, the decay factor, and the decay rate
In 1983 there were 141,200 bats living in the caves, which means that the initial amount is 141,200.
That number decreased by about 11% annually until 2003 means that the decay factor is 1 - 0.11 = 0.89 and the decay rate is 0.11 = 11%.
B. Write a function that models and number of that since 1983 then find the number of bats in 2003
With the data found in question A, we have that:
The function is
Number in 2003
2003 is 2003 - 1983 = 20 years after 1983, so this is y(20).
The number of bats in 2003 was of 13,729.