A is the doubling time for y=26e^0.5t, and B is the doubling time for y=13e^0.5t. Then
(a) A=2B
(b) B=2A
(c) A=B
(d) A=(ln2)B
The correct answer is A, right? I just want to make sure I got the correct answer.
nope. Both grow at the same rate: e^.05t
The population of A is 2*B but the growth rate is the same.
To determine whether option A is correct, let's first understand the concept of doubling time.
The doubling time of an exponential growth function represents the time it takes for the quantity to double in value. It is calculated by taking the natural logarithm of 2 divided by the coefficient of the exponential term.
For the function y = 26e^(0.5t), the doubling time (A) can be calculated as follows:
A = ln(2) / 0.5
A = 2ln(2)
Similarly, for the function y = 13e^(0.5t), the doubling time (B) can be calculated as:
B = ln(2) / 0.5
B = 2ln(2)
Now, let's compare the expressions for A and B:
A = 2ln(2)
B = 2ln(2)
As we can see, A is equal to B, so the correct answer is (c) A = B.
Therefore, the statement "A = 2B" (option A) is incorrect.