For the following exercises, start with the graph of $f(x)=4^{x}.$ Then write a function that results from the given transformation. Shift f(x) 3 units downward

For the following exercises, start with the graph of $f(x)=4^{x}.$ Then write a function that results from the given transformation. Shift f(x) 5 units right

For the following exercises, graph the transformation of $f(x)=2^{x}.$ Give the horizontal asymptote, the domain, and the range. $f(x)=2^{x-2}$

Kyoko has $\$ 10,000$ that she wants to invest. Her bank has several investment accounts to choose from, all compounding daily. Her goal is to have $\$ 15,000$ by the time she finishes graduate school in 6 years. To the nearest hundredth of a percent, what should her minimum annual interest rate be in order to reach her goal? (Hint: solve the compound interest formula for the interest rate.)

Alyssa opened a retirement account with $7.25 \%$ APR in the year $2000$. Her initial deposit was $\$ 13,500$. How much will the account be worth in $2025$ if interest compounds monthly? How much more would she make if interest compounded continuously?

For the following exercises, graph the transformation of $f(x)=2^{x}.$ Give the horizontal asymptote, the domain, and the range. $h(x)=2^{x}+3$

Jamal wants to save $54,000 for a down payment on a home. How much will he need to invest in an account with 8.2% APR, compounding daily, in order to reach his goal in 5 years?

For the following exercises, graph the transformation of $f(x)=2^{x}.$ Give the horizontal asymptote, the domain, and the range. $f(x)=2^{-x}$

For the following exercises, use the given information to find the unknown value. y varies jointly as the square of x and the square root of z. When x = 2 and z = 9, then y = 24. Find y when x = 3 and z = 25.

In the year $1985$, a house was valued at $\$ 110,000$. By the year $2005$, the value had appreciated to $\$ 145,000$. What was the annual growth rate between $1985$ and $2005$? Assume that the value continued to grow by the same percentage. What was the value of the house in the year $2010$?

For the following exercises, identify whether the statement represents an exponential function. Explain. For each training session, a personal trainer charges his clients $5 less than the previous training session.

The fox population in a certain region has an annual growth rate of $9 \%$ per year. In the year $2012$, there were $23,900$ fox counted in the area. What is the fox population predicted to be in the year $2020$?

Find the exact value. $\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)$

Determine whether the statement is true or false. If the $n \times n$ matrix A is idempotent and invertible, then A=I.