Answer:
k is 2.5.
Explanation:
To find the value of k, we can use the information given about points A and B to find the value of the parameters a and b. Since we know that the curve passes through A (1, 10) and B (4, 80), we can substitute these points into the equation y = ab^x to find the values of a and b.
Starting with point A:
10 = a * b^1
Next, using point B:
80 = a * b^4
We can now use these two equations to find the value of b:
10 = a * b^1
80 = a * b^4
Dividing the second equation by the first equation:
8 = b^3
Taking the cube root of both sides:
b = 2
We can now use either of the two equations to find the value of a:
10 = a * b^1
a = 10/2 = 5
Now that we have found the values of a and b, we can substitute the point C (-1, k) into the equation y = ab^x to find the value of k:
k = 5 * 2^(-1) = 5 * (1/2) = 2.5
So the value of k is 2.5.