Answer:
Step-by-step explanation:
The formula for <u>exponential growth</u> is y = ab^x.
To write this equation, we know it has to start with 48 (which is the variable a). We need to add the rate of growth. This is 11/6 (which is variable b). But we also need to account for the "every 3.5 years" part, so divide the x as an exponent by 3.5.
N(t) = 48 * 11/6^(t/3.5)
This equation is easy to test, and it's a good idea to test it after you write it. For example, after 3.5 years we know that it should have 48*11/6 branches. Does our equation work? Yes.
Answer:
a
The 95% confidence interval is 
b
The sample proportion is 
c
The critical value is 
d
The standard error is 
Step-by-step explanation:
From the question we are told that
The sample size is n = 200
The number of defective is k = 18
The null hypothesis is 
The alternative hypothesis is 
Generally the sample proportion is mathematically evaluated as
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
Next we obtain the critical value of 
from the normal distribution table, the value is
Generally the standard of error is mathematically represented as
substituting values
The margin of error is
=> 
=> 
The 95% confidence interval is mathematically represented as
=> 
=>
Answer:
Step-by-step explanation:
C
By definition, the average rate of change is given by:
We evaluate each of the functions in the given interval.
We have then:
For f (x) = x ^ 2 + 3x:
Evaluating for x = -2:
Evaluating for x = 3:
Then, the AVR is:
For f (x) = 3x - 8:
Evaluating for x =4:
Evaluating for x = 5:
Then, the AVR is:
For f (x) = x ^ 2 - 2x:
Evaluating for x = -3:
Evaluating for x = 4:
Then, the AVR is:
For f (x) = x ^ 2 - 5:
Evaluating for x = -1:
Evaluating for x = 1:
Then, the AVR is:
Answer:
from the greatest to the least value based on the average rate of change in the specified interval:
f(x) = x^2 + 3x interval: [-2, 3]
f(x) = 3x - 8 interval: [4, 5]
f(x) = x^2 - 5 interval: [-1, 1]
f(x) = x^2 - 2x interval: [-3, 4]
