Tavon has a gift card for $95 that loses $4 for each 30-day period it is not used. He has another gift card for $85 that loses $3.50 for each 30-day period it is not used. a. Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal.
b. What will the value of each card be when they have equal value?

20 periods, $15

Step-by-step explanation:

We can set up 2 equations for each card.

The first is 95-4x

x represents each 30 day period.

The second equation is 85-3.5x

95-4x=85-3.5x

95=85+.5x

10=.5x

x=20

It will take 20 periods til they equal each other.

We plug in 20 for x to find the value.

95-4(20)=15

They will be at $15

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50