Question

Enter the function below in the form p=p0at. Does it represent exponential growth or exponential decay? P=2e−0.5t round the base of the exponential function, a, to four decimal places

Answer 1

we are given

$P=2e^{-0.5t}$

we have to write this in

$P=P_0a^{t}$  form

we can rewrite our function as

$P=2(e^{-0.5})^t$

we can simplify value inside parenthesis

we get

$P=2(0.6065)^t$

now, we can compare it with

$P=P_0a^{t}$  form

and find 'a'

we get

$a=0.6065$

Since,

$a=0.6065$

so, this is exponential decay function.........Answer