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?

Quote:

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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?

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I assume that you mean:

$\displaystyle y = 100 \cdot e^{-0.076 \cdot t} = 100 \cdot \left(e^{-0.076}\right)^t = 100 \cdot 0.9268^t$

i meant this sorry i wrote it wrong.

y=100e^(-0.07t)

Quote:

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Originally Posted by Kate182

i meant this sorry i wrote it wrong.

y=100e^(-0.07t)

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$\displaystyle y=100\cdot e^{-0.07t} = 100\cdot \left(e^{-0.07}\right)^t = 100\cdot 0.9324^t$

How do i find the growth or decay rate then?

Quote:

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Originally Posted by Kate182

How do i find the growth or decay rate then?

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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:

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

I've got $\displaystyle 6.76 \%$

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