Question

If you write the function P=10e^−2t in the form P=P0a^t, then what is P0 and a?

Answer 1

i know P0 is equal to 10 but not sure what a is equal to

Answer 2

this also shows decay

Answer 3

the trick is to use this idea with exponents
\[ \left(a^b\right)^c = a^{bc} \]

Answer 4

or I should say, the other way round:
\[ a^{bc}=\left(a^b\right)^c \]
notice we can match e with the "a" ,-2 with b, and "t" with c in
\[ e^{−2t} \]
can you rewrite this to show the "t" "pulled out" like in
\[ a^{bc}=\left(a^b\right)^c \]?

Answer 5

if it doesn't show, refresh your browser.

Answer 6

(a^-2)^t @phi ?

Answer 7

almost. it is still "e"
(e^-2)^t

the the stuff in the parens e^-2 is a number. Use a calculator or type
e^-2 =
into google

Answer 8

in other words
\[ 10 e^{-2t} = 10 \ \left( e^{-2}\right)^t \\ = 10 (0.13533)^t \]

Answer 9

roughly... e^-2 goes on forever, so we have to stop at some point.

it's now in this form
P=P0 a^t

and as you already know P0 = 10
and a = e^-2 = (about) 0.13533...