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squidhardy:
The initail value of a car is $25,000. After one year, the value of the car is $21,250. Write an exponential function to model the expected value of the car. Estimate the value of the car after 5 years.

Hi Squidhardy and CPhill
there is a formula but I want to show you the logic behind it.
Say the deflation rate is r per year. This will mean the following

Original value = $25000
After 1 yr = $25000 * (1-r)
After 2 yr = $25000 * (1-r) ²
After 3 yr = $25000 * (1-r) ³
After 4 yr = $25000 * (1-r) ⁴
After 5 yr = $25000 * (1-r) ⁵
After n years = $2500 * (1-r) ⁿ

the general formula is F _n=P(1-r) ⁿ
Where F is future value and P is the principal value.

so we have
F _n = $25000 * (1-r) ⁿ
and
$25000 * (1-r) = $21,250 [Value after 1 year is used to find r]
1-r = 21250/25000
1-21250/25000=r

1-21250/25000
So the car is depreciating by 0.15 or 15% per year.
1-0.15=0.85

F _n = $25000 * 0.85 ⁿ
F ₅ = $25000 * 0.85 ⁵

25000*0.85^5

So after 5 years the car will be worth $11092.63

MelodyMar 21, 2014

+118725

That is if it shared equally

MelodyMar 21, 2014

Mar 20, 2014

GuestMar 20, 2014

+118725

CountryGirl333:
Find the height of a triangular prism with a base length of 10 yards, a base height of 20 yards, and a volume of 600 cubic yards.

Sorry Sam but it is a prism NOT a pyramid so you have used the wrong formula.

The volume of any prism is the area of the cross section (that stays the same) times by the depth, or height or whatever you want ot call it.

I think it is the height of the triangle that is missing although the question could be interpreted differently. The area of a triangle is (1/2)*base*height = (1/2) * 10 * h = 5h yards squared

so
5h*20=600
and you can finish it.

MelodyMar 20, 2014

+130561

I think I remember how to do this from my college Physics class many years ago. (Any Physics pros on the forum can double-check me!!)

We need to find a constant - call it "k'

We have

D = k(S^2)

200 = k(60^2)

200 = k(3600)

k = 200 / 3600 = 1 / 18

So we have

D = (S^2) / 18

I think you can take it from here......

CPhillMar 20, 2014

+130561

FYI......here's a site that will calculate a binomial expansion for you......I think it gives some other info too, but I didn't look closely!!

http://calculator.tutorvista.com/math/597/binomial-expansion-calculator.html

(I meant to include this with my previous answer, but I forgot!!!)

CPhillMar 20, 2014

+130561

what's the binomial expansion of (2x-3y) to the third power??

(1)*(2x)^3*(-3y)^0 + (3)*(2x)^2*(-3y)^1 + (3)*(2x)^1*(-3y)^2 + (1)*(2x)^0*(-3y)^3 =

8x^3 - 36(x^2)(y) + 54(x)(y^2) - 27(y^3)

Note that the sum of the powers in each term always = the degree of the expansion (3, in our case)

Also, the coefficients in the first expression come from the row number in Pascal's Triangle that equals the degree of the expansion - assuming that the "1" at the top of the triangle is Row "0" (We can also find them through a combinatoric formula that I'm too lazy to summon!!)

Hope this helps and I pray I got all my parenthesis typed in correctly!!!

CPhillMar 20, 2014

+130561

As long as x isn't = 0 (and it's not) we have a solution (or two)

First, multiply through by x

This gives us

x^2 +109.9 = 6.7x

Rearranging, we have

x^2 - 6.7x + 109.9 = 0

Let's multiply everything by 10 to get rid of those pesky decimals!!
This gives us
10x^2 - 67x + 1099 = 0

This might factor, but somehow, I doubt it!!

I can tell that we have - possibly - either two positive solutions or zero positive solutions. Further, there are no negative solutions. (If you take pre-calculus, you'll find out why this is true!!)

I see something else, too. If i square (-67), I get 4489. If I multiply the last term, times the first term, times (-4), I get (1099)*(10)*(-4) = -43960. Adding this to 4489 gives me -39471, and this would be the term under the radical in the quad formula. Therefore, since we will get a negative quantity under a square root, we don't have a real number solution.

Just for the heck of it, let's see what the quad formula would produce!!

10x^2 - 67x + 1099 = 0

Yep...just as we expected.......no real solutions!!!

This just proves that a little analysis sometimes is more important than worrying about the "right" answer!!

Hope this helped you!!

CPhillMar 20, 2014

+130561

Note that this factors into

(9x + 8) (9x + 8) = 0 (A perfect square trinomial)

Can you take it from there???

CPhillMar 20, 2014

+33666

samgelinas:
amber6198:
:? The logistic growth function f(t)=67000/1+1339.0e^-0.11t models the numbers of people who have become ill with a particular infection t weeks after its initial outbreak in a particular community. How many people become ill with this infection when the epidemic began?
A) 67,000 people
B) 1340 people
C) 50 people

You only need to replace "t" by "0" in your equation, because "t" it's for the time.

So at the time "0" you'll have 67 000 peoples infected.

Right principle, but wrong answer because the function is written incorrectly! The function should be f(t)=67000/(1+1339e ^-0.11t).
So, when t = 0, we have f(0) = 67000/(1+1339) or

67000/1340

AlanMar 20, 2014

+130561

Formula for calculating simple interest:

I = Prt

Where,
I = interest
P = principal
r = interest rate (per year)
t = time (in years or fraction of a year)

So we have

29750 = P(,05)(7)

Solving for P

P =

(29750)/(.05*7)

...........$85000.........

CPhillMar 20, 2014

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