Write and Graph a function that represents the situation. Your $35,000 annual salary increases by 4 percent each year.
And your thinking is....?
To write and graph a function that represents the situation, we can use the concept of compound interest.
The formula for compound interest is given by:
A = P(1 + r/n)^(nt)
where:
A is the final amount (in this case, the annual salary),
P is the initial amount (in this case, $35,000),
r is the interest rate (in this case, 4% or 0.04),
n is the number of times the interest is compounded per year (since it is an annual salary, n = 1),
t is the number of years.
So, in this case, the function that represents the situation is:
f(t) = 35,000(1 + 0.04/1)^(1t)
Simplifying the function:
f(t) = 35,000(1 + 0.04)^t
f(t) = 35,000(1.04)^t
Now, let's graph this function to see how the salary increases over time.
To graph the function, we can choose different values for t (number of years) and calculate the corresponding salaries using the function f(t).
For example, let's calculate the salary after 10 years:
f(10) = 35,000(1.04)^10 = 52,205.27
Similarly, you can calculate the salaries for other values of t.
Once you have calculated the salaries for different values of t, you can plot the coordinates (t, f(t)) on a graph to visualize the increase in salary over time.
Remember to label the x-axis as "Years" (t) and the y-axis as "Salary" (f(t)). Use the calculated values to plot the points and connect them to form a smooth curve to represent the function.