function

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Oct 13th 2008, 08:05 PM
Kate182

function

So they give me this

Y=100e^(-0.076)

Write the exponential function in the form y=ab^t. Find b accurate to four decimal places. If t is measured in years, give the percent annual growth or decay rate and the continuaous percent growth or decay rate per yer.

Isn't it already in the form they ask me to put it in?
Oct 13th 2008, 09:44 PM
earboth

Quote:

Originally Posted by Kate182

So they give me this

Y=100e^(-0.076)

Write the exponential function in the form y=ab^t. Find b accurate to four decimal places. If t is measured in years, give the percent annual growth or decay rate and the continuaous percent growth or decay rate per yer.

Isn't it already in the form they ask me to put it in?

I assume that you mean:

$y = 100 \cdot e^{-0.076 \cdot t} = 100 \cdot \left(e^{-0.076}\right)^t = 100 \cdot 0.9268^t$
Oct 13th 2008, 09:50 PM
Kate182

i meant this sorry i wrote it wrong.

y=100e^(-0.07t)
Oct 13th 2008, 10:01 PM
earboth

Quote:

Originally Posted by Kate182

i meant this sorry i wrote it wrong.

y=100e^(-0.07t)

$y=100\cdot e^{-0.07t} = 100\cdot \left(e^{-0.07}\right)^t = 100\cdot 0.9324^t$
Oct 13th 2008, 10:10 PM
Kate182

How do i find the growth or decay rate then?
Oct 13th 2008, 10:44 PM
earboth

Quote:

Originally Posted by Kate182

How do i find the growth or decay rate then?

If t = 0 you have y = 100;

if t = 1 you have y = 93.24.

Thus you have an absolute decay of d(1) = 6.76

Now calculate the relative decay:

$r = \dfrac{d(1)}{y(0)}\cdot 100$

I've got $6.76 \%$
Oct 13th 2008, 10:54 PM
Kate182

So that would be the annual growth rate right?
what about the continuous, is it the same?

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