Answer:
6.174 x 10^11
Explanation:
We can find the value of k by substituting a known value of x and solving for k.
Let's choose x = 0, then:
f(0 + 3) = (0)² + ke-21
f(3) = ke-21
Since we don't know the value of f(3), we cannot solve directly for k. However, we can use another piece of information: the function f(x) is defined as f(x) = x³ - 1.
Let's substitute x = 0 into the definition of f(x):
f(0) = 0³ - 1
f(0) = -1
Now, we can use this information to find f(3):
f(3) = (3)³ - 1
f(3) = 27 - 1
f(3) = 26
Substituting this back into the original equation:
f(3) = ke-21
26 = ke-21
Solving for k:
k = 26e^21
Therefore, the value of k is approximately 6.174 x 10^11.