The general formula for exponential growth and decays is:
if k>0 then then it is an exponential growth function. If k<0 then the function represents an exponential decay.
Now we need to classify each of the functions:
1.
The function
can be wrtten as:
comparing with the general formula we notice that k=2, therefore this is an exponential growth.
2.
The function
can be written as:
comparing with the general formula we notice that k=-4, therefore this is an exponential decay.
3.
The function
comparing with the general formula we notice that k=-1, therefore this is an exponential decay.
means there exists an integer
such that
. We can divide both sides by
because
. This implies
for some integer, which is identically
.
Answer: Prokhorova is more outstanding.
Step-by-step explanation: To compare scores from different distributions, first standardize it:
z-score = 
where
x is the individual mean you want to compare
μ is the mean of the population
σ is standard deviation
For <u>Gertrud Bacher</u>:
z-score = 
z-score = 
(s)
The negative sign indicates Bacher's mean is less than the mean
For <u>Yelena Prokhorova</u>:
z-score = 
z-score = 2 (cm)
The positive sign indicates Prokhorova's mean is more than the mean.
Using z-score table, you determine the percentiles are:
For Bacher: Percentile = 5.5%
For Prokhorova: Percentile = 97.7%
Bacher's percentile means she is above 5.5% of the participants, while Prokhorova is 97.7% above the other competitors, which means Prokhorova have a better performance and deserves more points.
Answer:
positive correlation, causal
negative correlation, not causal
negative correlation, causal
Step-by-step explanation:
Answer: 8+(x÷39) or (x÷30)+8
