The number of employees of a national company is given by N(t) = 60(1 .02)^{t} where N(t) is the number of employees in thousands,t years since 2005.

The function ${\displaystyle y=3.5x+2.8}$ represents the cost y (in dollars) of a taxi ride of x miles.
a. Identify the independent and dependent variables.
b. You have enough money to travel at most 20 miles in the taxi. Find the domain and range of the function.

A city water department is proposing the construction of a new water pipe, as shown. The new pipe will be perpendicular to the old pipe. Write an equation that represents the new pipe.

Colleen and Martin are modeling the data shown. Colleen thinks the model should be ${\displaystyle f\left(x\right)={5.754}^{x}3+2.912x^2-7.516x0.349}$. Martin thinks it should be ${\displaystyle f\left(x\right)=3.697x^2+11.734x-2.476}$. Is either of them correct? Explain your reasoning.
f(x) -2-190.5-2 -1511.5 00.4243

A toy rocket (not internally powered) is launched straight up from the top of a building 50 ft tall at an initial velocity of 200 ft per sec.
a) Give the function that describes the height of the rocket in terms of time t.
b) Determine the time at which the rocket reaches its maximum height and the maximum height in feet.
c) For what time interval will be rocket be more than 300 ft above ground level?
d) After how many seconds will it hit the ground?

Consider a 3000 lb car whose speed is increased by 30 mph. Modeling the car as a particle and assuming that the car is traveling on a rectilinear and horizontal stretch of road, determine the amount of work done on the car throughout the acceleration process if the car has an initial speed of 45 mph.

Values of the following expressions:
a) ${\displaystyle (g\cdot f)\left(0\right)}$
b) ${\displaystyle (f\cdot g)\left(5\right)}$
c) ${\displaystyle (g\cdot g)\left(10\right)}$

The area (in square feet) of the school sign can be represented by ${\displaystyle 15x^2-x-2}$.
a. Write an expression that represents the length of the sign.
b. Describe two ways to find the area of the sign when ${\displaystyle x=3}$.