Find the continuous growth rate is Q=7000e^(0.24t)
e^rt has a growth rate of r, so that would be .24=24%
To find the continuous growth rate, we can use the formula A = P * e^(rt), where A is the final amount, P is the initial amount, r is the growth rate, and t is the time.
In your equation, Q = 7000e^(0.24t), Q represents the final amount, and r is the growth rate.
To find the growth rate, we can compare this equation to the general formula A = P * e^(rt).
Comparing the two equations, we can see that:
Q = 7000e^(0.24t) = P * e^(rt)
P represents the initial amount, so we can assign P = 7000.
Then, Q = 7000e^(0.24t) becomes:
7000e^(0.24t) = 7000 * e^(rt)
Divide both sides of the equation by 7000:
e^(0.24t) = e^(rt)
Since the base of the natural logarithm, e, is the same on both sides of the equation, we can equate the exponents:
0.24t = rt
Divide both sides of the equation by t and by r:
0.24 = r
Therefore, the continuous growth rate, r, is 0.24, or 24%.