Let's say that the value of a car over time is given by the equation: y = 20,000 (.88)
Tell me the following two things:
a) Is this a growth or decay problem and why?
b) What is the percent amount that the value changes by each year?

Step-by-step explanation:

So bascially decay means shrinks or shrivels. Growth means like growing, bigger, sort of like a happy plant :D.

To find if this is getting bigger or is shrinking, lets plug in something simple like 1 for the time(t). Sooo:

20,000*.88^1

Since its a 1 exponent it does nothing so:

20,000*.88

Now this is 17600 you can use calculator but if you do this in head like me all I did is multiply 88 by 2 which was simply since 8 times 2 is 16 so 160+16 is 176 then I added zeros:

y=17600

As we can see this is smaller than 20,000, so it is a decaying problem.

By what percent tho.

Well this is pretty easy to reconize once you understand where to find it.

When they talk about percentage, they mean how much it decreased by.

This is 100%-the multiplyied value.

In this case the multiplyed value is 0.88, sooo:

100%-88%=18%

So the percent amount that the value decreased by is 18%.

Hope this helps!

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.