Help with this ONE pre-calc problem--I dont usually use Y! Answers for help with math. PLEASE HELP!?

Question

Because of a slump in the economy a company finds that its annual profits have dropped from $742,000 in 1998 to $632,000 in 2000. If the profit follows an exponential pattern of decline, what is the expected profit for 2001. Let t=0 represent 1998.


I think I have to use the Pe^rt formula, but I don't know how to go about it.

Answer 1

yes you do need to use that formula.

So $632,000 = $ 742,000 e^r2

.8517520216= e^r2

r= -.0802299245
now you can use the formula again but because you have the rate you can solve for 2001, because 2001 is 1 yr after 2000 use the amount $632,000 this time.

A = $632,000e^-.0802299245(1)

A= $583275.40

Answer 2

(1) The easy way:

In TWO years (that's the tricky part), the decline is 632000/742000. However, since it is two years, that is the SQUARE of the per-year decline, given exponential decline.

Two-year decline = 632000/742000
Two-year decline = 0.85175

One-year decline = sqrt(0.85175) = 0.9229

The estimate for 2001 is sqrt(0.85175) * 632000 (the 2000 value), or 583,275.

(2) The right way:

In year t, profits = Pe^rt

t=0 (1998), profits = Pe^rt = Pe^r*0 = P.
Since profits = 742000, P=742000

t=2 (2000), profits = Pe^rt = Pe^2r = 742000e^2r
Since profits = 632000...

632000 = 742000e^2r
ln(632000/742000) = 2r
-0.16046 = 2r
-0.08023 = r

Now we have the equation with only t remaining as a variable:

Profits(t) = 742000 * e^(-0.08023 * t)

For 2001, t=3:

Profits(3) = 742000 * e^(-0.08023 * 3)
Profits(3) = 742000 * e^(-0.24069)
Profits(3) = 742000 * 0.786085
Profits(3) = 583,275

Answer 3

742,000 / 632,000 = 1.174
sqrt(1.174)=1.0835
742,000/1.0835=684794.86
684794.86/1.0835=632,000
632,000/1.0835=583,275.41

t=0 (1998) : $742,000
t=1 (1999) : $684,794.86
t=2 (2000) : $632,000
t=3 (2001) : $583,275.41

Answer 4

if the total decline from 1998 to 2000 was 110,000 .. that is in two yrs. so the total decline for one yr would be 55,000 so im guessing that is your answer divide 110,000 by 2 to figure out what the decline is for one yr

Answer 5

P2=P0*exp(r*2) <=>
r=1/2 * ln(P2/P0)

P3 = P2 * exp(r)

r = -0.0802299
P3=583.275

Answer 6

gl there are some good answers in here.