Answer:
Her grant in four years time will be of $13108.
Step-by-step explanation:
Exponential equation:
An exponential equation has the following format:

In which A(0) is the initial value and r is the growth rate, as a decimal.
A student get a grant of $10000 a year assuming her grant is increased by 7% each year
This means that 
So



What will her grant be in four years time?
This is A(4). So


Her grant in four years time will be of $13108.
Scale factor = 12 ÷ 6 = 2
61 ÷ 2 = 30.5 units
The given function is
f(x)= 0.2 x²
Since f(x) will be defined for all real values of x.
So, Domain of f(x) will be ( x| x is a real number.)→This is set builder notation.
Finding the inverse of f(x):
y = 0.2 x²
→ x²= 5 y
→x =
→ → Inverse of f(x)
Replacing x by y and y by x,we get inverse of the given function
y =
→ →Domain x ≥ 0, x∈[0,∞]
Graph of function and its inverse are shown below.
Using the Empirical Rule and the Central Limit Theorem, we have that:
- About 68% of the sample mean fall with in the intervals $1.64 and $1.82.
- About 99.7% of the sample mean fall with in the intervals $1.46 and $2.
<h3>What does the Empirical Rule state?</h3>
It states that, for a normally distributed random variable:
- Approximately 68% of the measures are within 1 standard deviation of the mean.
- Approximately 95% of the measures are within 2 standard deviations of the mean.
- Approximately 99.7% of the measures are within 3 standard deviations of the mean.
<h3>What does the Central Limit Theorem state?</h3>
By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
In this problem, the standard deviation of the distribution of sample means is:

68% of the means are within 1 standard deviation of the mean, hence the bounds are:
99.7% of the means are within 3 standard deviations of the mean, hence the bounds are:
More can be learned about the Empirical Rule at brainly.com/question/24537145
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