Q = 16.8*10^-0.22t
Give the starting value a, the growth rate r, and the continuous growth rate k.
Exact answer for a, Round the answer for r and k to two decimal places
a = 16.8
r = 10
k = -22%
Can someone check my answer? I do not think the values for r and K are correct. I think the -0.22t is throwing me off
Hey, I just did two of these, please use one name and do not ask me to do a whole bunch of virtually identical problems.
To find the starting value (a), growth rate (r), and continuous growth rate (k), let's analyze the given equation:
Q = 16.8 * 10^(-0.22t)
The formula you provided can be rewritten as:
Q = a * r^t
where a represents the starting value, r represents the growth rate, and t represents time. By comparing the two equations, we can determine the values for a, r, and k.
Starting value (a):
In the given equation, the starting value (a) is equal to 16.8.
Growth rate (r):
To find the growth rate (r), we need to isolate it from the equation. Let's rewrite the equation as:
Q = a * r^t
Divide both sides of the equation by a:
Q / a = r^t
To determine r, we can take the t-th root of both sides of the equation:
r = (Q / a)^(1/t)
In this case, you mentioned t = 10. Plugging in the values, we get:
r = (16.8 * 10^(-0.22*10))^(1/10)
= (16.8 * 10^(-2.2))^(1/10)
= (16.8 * 0.00630957344480193)^(1/10)
= 0.6667438154472616
Hence, the growth rate (r) is approximately 0.67 (rounded to two decimal places).
Continuous growth rate (k):
The continuous growth rate (k) can be found using the formula:
k = ln(r)
where ln represents the natural logarithm function. Plugging in the value we found for r:
k = ln(0.67)
≈ -0.400477566
Note that the value of k is not -22%, as you mentioned. Instead, it is approximately -0.40.
Therefore, the correct values are:
a = 16.8
r ≈ 0.67
k ≈ -0.40