I need help with my algebra homework desperately I need it please as soon as possible please respond

Question

1.) The value of a car bought new for $28900 decreases 15% each year. Identify the function for the value of the car. Does the function represent growth or decay?

A.) V(t) = 28900(0.15)t; decay

B.) V(t) = 28900(0.85)t; decay

C.) V(t) = 28900(0.85)t; growth

D.) V(t) = 28900(0.15)t; growth

2.) The pressure P exerted by a force varies inversely as the area A on which the force is applied. If 16 N/ft2 of pressure is exerted by a force on an area of 3 ft2 , what is the pressure exerted by the same force on an area of 6 ft2?

A.) 16 N/ft2

B.) 8 N/ft2

C.) 32 N/ft2

D.) 4 N/ft2

Answer 1

1) V(t) = P ( 1- r ) ^t

where P is the original price, r is the percent rate of decrease , and t is the time

V(t)= 28,900 ( 1 - 0.15 ) ^t

V(t)= 28,900 ( 0.85 ) ^t

And this will Decay with time because the value of ( 0.85 ) ^t decrease when t increase.

2) p = k / A

P₁ = K / A₁

P₂ = K / A₂

P₂ / P₁ = A₁ / A₂

P₂ = P₁ A₁ / A₂

= 1 6 * 3 / 6

= 8 N/ ft²

Answer 2

1. B. The way to think about this is to do a few examples and then see the pattern. In the first year, we know the car values goes down by 15%, So it goes down by 28,900*0.15. But that means the new value after one year is 28900 - 28900 *0.15. Taking the 28000 in common and factoring (there is a reason for this hold on), it becomes 28900(1-0.15) = 28900 * 0.85. Good, now in the second year, the same thing happens, so it starts at 28,900 *0.85 and goes down up by 15% so the value now goes down to 28900*.85 - 28900*.85 * 15. Again, taking the 28000 *0.85 common the value is now 28900*..85 (1 - 1.15) = 28900 * (0.85)*).85 = 28000 * (0.85)^2. So after one year it is 28000 *0.85 after two years it is 28900 * (0.85)^2, . . . it's easy to guess the pattern and see that after three years it becomes (28900)*(0.85)^3 and after t years it becomes (28900)*(0.85)^t and its clearly decreasing in value, so the answer is B. Its also a standard formula but its easier to understand how to do this a few times so it becomes second nature.
2. B. The way to think of direct proportion using ratios and inverse proportion by multiplication. If by some chance pressure was directly proportional to area we would set up a standard proportion of the kind you have probably seen before: P1/A1 = P2/A2. But because its an inverse proportion, we do the same thing with multiplication instead of division so we get P1 * A1 = P2 * A2. This makes sense because it means that if P2 is bigger than P1 then A2 will be smaller than A1 which is why its inversely proportional. Once you've seen this its time to plug and play. We know P1 = 16 and A1 = 3 and we know A2 = 6 (lets ignore units for now). So 16 * 3 = P2 * 6, so P2 = 8. A quicker way of doing this that really helps in speed tests is to realize that the area has doubled so the pressure must have halved (because its inverse proportion, it would have been the opposite for direct proportion), So the new pressure must be half the old pressure which was 16 and so is now 8. After some practice, you can do these kind of problems (where the ratios are simple) in your head and oddly enough its less error prone that writing algebra that you can sometimes manipulate wrongly. So the answer is B again! Oh and you can bring back the units at this point and so its 8 N/feet squared (you don't have to understand the physics, it's a math class after all, so just copy the units of P1).

Answer 3

For #1. You would take the $28,900 would be your initial value and 15% decrease would be your rate. In order to figure out what would be inside the parentheses you would take 15% and convert it to a decimal. This would be 15%=.15. From there you would subtract 1 and our rate together which would be equal to 1-.15=.85. The correct answer would be letter B, and the function would be decay because .85 ( the number inside the parentheses) is less than 1.

For #2. We see that if 16 N/Ft^2 of pressure the area is 3 Ft^2. So if we have the area of 6 ft^2, the pressure would be doubled of the pressure when the area was 3ft^2. So 16 doubled would be 32. Therefore the answer is letter C.