# function

• 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:

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

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

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

I've got $\displaystyle 6.76 \%$
• Oct 13th 2008, 10:54 PM
Kate182
So that would be the annual growth rate right?
what about the continuous, is it the same?