Convert Q = 17(0.887)^1.2t to the form
Q = ae^kt
Round all calculated values to three decimal places
Q = ?
My answer was 17e^-0.099t, but I do not think that it is correct
I don't know math because im dumb
.887 = e^-.1199, so
.887^1.2t = e^(-.1199*1.2t) = e^-.144t
It's always better to show your work, so we can help correct the errors, if any.
To convert the given equation Q = 17(0.887)^1.2t to the form Q = ae^kt, we need to express it in terms of the exponential function.
First, let's simplify the given equation. Applying the exponent rule of (a^b)^c = a^(bc), we can rewrite the equation as:
Q = 17((0.887)^1.2)^t
Now, let's evaluate the exponential term (0.887)^1.2:
(0.887)^1.2 = 0.681
Substituting this value back into the equation, we have:
Q = 17(0.681)^t
To express this in the form Q = ae^kt, we need to rewrite (0.681)^t in terms of the exponential function.
To do this, we can use the property of exponential functions, which states that a^x = e^(ln(a)*x).
Therefore, (0.681)^t = e^(ln(0.681)*t).
Now, let's evaluate ln(0.681):
ln(0.681) ≈ -0.385
Substituting this value back into the equation, we have:
Q = 17e^(-0.385t)
Therefore, the correct expression for Q is Q = 17e^(-0.385t), not 17e^-0.099t.
Please note that the rounded values are not used in the calculation, only for the final expression.