Question

graph the following equations.
7.) juan makes minimum wage, which is $15.50
dollars an hour. record how much money he’d
earned (f(x)) if he worked x hours.
write an equation to represent this:

x	f(x)
1
2
3
4
5

graph grid

how much money will he make after working a
40-hour week?

8.) scientists were studying a population of rabbits.
their population had dwindled to only 8 rabbits.
through conservation efforts, the rabbit population
began to triple each year!

write an equation to represent this:

x	f(x)
1
2
3
4
5

graph grid

how big would the rabbit population be in a decade?

Explanation:

Problem 7 (Juan's Earnings)

Step1: Define the function

Juan earns $15.50 per hour. So the total earnings \( f(x) \) for \( x \) hours is \( f(x) = 15.50x \).

Step2: Calculate for 40 hours

Substitute \( x = 40 \) into the function: \( f(40) = 15.50 \times 40 \).
\( 15.50 \times 40 = 620 \).

Step1: Define the exponential function

The initial population (when \( x = 0 \)) is 8, and it triples each year. So the function is \( f(x)=8\times3^{x} \), where \( x \) is the number of years.

Step2: Calculate for a decade (10 years)

Substitute \( x = 10 \) into the function: \( f(10)=8\times3^{10} \).
First, calculate \( 3^{10}=59049 \). Then, \( 8\times59049 = 472392 \).

Answer:

The equation is \( f(x) = 15.50x \), and he will make $620 after a 40 - hour week.

Problem 8 (Rabbit Population)