The cost of an lcd tv dropped from $825 in 2012 to $575 in 2014. construct a linear model to predict the cost of an lcd tv and use it to predict the cost of a tv in 2015.

The cost of an LCD TV dropped from $825 in 2012 to $575 in 2014

Since it is a linear model, the rate of change of cost is constant

So rate of change (slope) = = -125

To find the cost of every year we subtract 125 from the cost of previous year

In 2014, the cost of an LCD TV = $575

In 2015, the cost of LCD TV  = $575 - 125 = $450

the cost of a TV in 2015 is $450

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).