Question

1. statistics two car manufacturers in the south bay, honda and toyota, recently released their new line of vehicles 2017

honda currently has 1500 employee in the south bay plant. when the new line of vehicles was released to the public, sales didnt go so well and sales began to drop. if honda sales continue to drop, its workforce will decrease by 150 employees per month.
on the other hand, when the new line of vehicles was released to the public, sales began to increase for toyota.
toyota currently has 400 employees and toyota plans to increases its workforce by 13% each month if their sales continue to increase.

at this rate, when will toyota have more employees?
a. write an equation to represent honda’s total number of employees per month.
h(m) =
c. write an equation to represent toyota’s total number of employees per month.
t(m) =
b. complete the table of values for honda’s workforce
d. complete the table of values for toyota’s workforce

months	number of employees		months	number of employees
--------	---------------------		--------	---------------------

e. let the x - axis represent the number of months and the y - axis represent number of employees. graph and label both functions on the graph below

at this rate, when will toyota have more employees? justify your reasoning by using mathematical language including but not limited to, linear, exponential and rate.

Explanation:

Part a: Honda's Employee Equation

Step1: Identify the type of function

Honda's workforce decreases by a constant number (150) per month, so it's a linear function. The general form of a linear function is \( H(m) = b - rm \), where \( b \) is the initial number of employees, \( r \) is the rate of decrease, and \( m \) is the number of months.

Step2: Plug in the values

Initial employees (\( b \)) = 1500, rate of decrease (\( r \)) = 150. So the equation is \( H(m) = 1500 - 150m \).

Step1: Identify the type of function

Toyota's workforce increases by a percentage (13%) per month, so it's an exponential function. The general form of an exponential growth function is \( T(m) = a(1 + r)^m \), where \( a \) is the initial number of employees, \( r \) is the growth rate, and \( m \) is the number of months.

Step2: Plug in the values

Initial employees (\( a \)) = 400, growth rate (\( r \)) = 0.13 (since 13% = 0.13). So the equation is \( T(m) = 400(1 + 0.13)^m = 400(1.13)^m \).

Step1: For \( m = 0 \)

Substitute \( m = 0 \) into \( H(m) = 1500 - 150m \). \( H(0) = 1500 - 150(0) = 1500 \).

Step2: For \( m = 1 \)

\( H(1) = 1500 - 150(1) = 1500 - 150 = 1350 \).

Step3: For \( m = 2 \)

\( H(2) = 1500 - 150(2) = 1500 - 300 = 1200 \).

Step4: For \( m = 3 \)

\( H(3) = 1500 - 150(3) = 1500 - 450 = 1050 \).

Step5: For \( m = 4 \)

\( H(4) = 1500 - 150(4) = 1500 - 600 = 900 \).

Answer:

\( H(m) = 1500 - 150m \)

Part c: Toyota's Employee Equation