If you write the function P=10e^−2t in the form P=P0a^t, then
P0=
a=
.
come on now !!
Did not notice the change in the exponent.
so
P=10e^−2t
= 10(e^-2)^t
= 10(1/e^2)^t
now compare with P=P0a^t
To write the function P = 10e^(-2t) in the form P = P0a^t, we need to find the values of P0 and a.
The general form of the exponential function is P = P0a^t, where P0 is the initial value of P when t = 0, and a is the base of the exponential function.
In our case, P = 10e^(-2t). To write it in the form P = P0a^t, we can compare it to the general form:
P0a^t = 10e^(-2t)
From the equation, we see that the initial value P0 is 10, and the base a is e^(-2).
Therefore:
P0 = 10
a = e^(-2)
So, P0 = 10 and a = e^(-2).
To write the function P=10e^(-2t) in the form P=P0a^t, we need to determine the values of P0 and a.
To do this, we can compare the given function to the desired form and equate the corresponding parts.
First, let's observe the given function, P=10e^(-2t). We can see that P0 is not explicitly given, but it represents the initial value of P when t=0.
In the desired form P=P0a^t, the base, a, represents the exponential growth rate or decay factor. In this case, we can determine it by observing the exponent of the given function.
Comparing the given function to the desired form, we see that P0 is missing. However, we can assume that P0=10, as it represents the initial value when t=0.
Now, let's rewrite the function using the identified values:
P=10e^(-2t) can be rewritten as P=10*(e^(-2))^t.
Now, we can see that a is equal to e^(-2). So, a=e^(-2).
In summary:
P0 = 10
a = e^(-2)