Question

thinking

1. 12 years ago, a house was worth $467000. the value of the house is now $845000. determine the houses appreciation rate assuming that the house increases in value at a constant rate every year. show your steps. t5

1. a. write two other equations that are equivalent to \\(y = 2401^x\\) t2

b. describe any transformations that correspond to the new equations t2

c. state the domain, range and the equation of the horizontal asymptote for each equation. t3

Explanation:

Solve for the appreciation rate in Question 10

$$
LATEXBLOCK0
$$

Find equivalent equations for Question 11a

$$
LATEXBLOCK1
$$

Describe transformations for Question 11b

$$
LATEXBLOCK2
$$

State domain, range, and asymptote for Question 11c

$$
LATEXBLOCK3
$$

Answer:

Question 10

The house's appreciation rate is approximately \(5.06\%\) per year.

Question 11

a.

Two equivalent equations are:

1. \(y = 7^{4x}\)
2. \(y = 49^{2x}\)

b.

• For \(y = 7^{4x}\), the graph is horizontally compressed by a factor of \(\frac{1}{4}\) compared to the parent function \(y = 7^x\).
• For \(y = 49^{2x}\), the graph is horizontally compressed by a factor of \(\frac{1}{2}\) compared to the parent function \(y = 49^x\).

c.

For all three equivalent equations (\(y = 2401^x\), \(y = 7^{4x}\), and \(y = 49^{2x}\)):

• Domain: \((-\infty, \infty)\)
• Range: \((0, \infty)\)
• Horizontal Asymptote: \(y = 0\)