The graph of an exponential function passes through the points (
–
1,10) and 1,2/5
. Write an equation for the function in the form y=a(b)x.
y=
To find the equation of the exponential function in the form y = a(b)^x, we need to find the values of a and b.
Using the point (-1, 10):
10 = a(b)^(-1)
10 = a/b
Using the point (1, 2/5):
2/5 = a(b)^1
2/5 = ab
Now we have a system of equations:
10 = a/b
2/5 = ab
We can solve this system by substituting the value of a/b from the first equation into the second equation:
2/5 = (10 * b)/b^2
2/5 = 10/b
2b = 50
b = 25
Substituting b = 25 into the first equation:
10 = a/(25)
10 * 25 = a
250 = a
Therefore, the equation of the exponential function in the form y = a(b)^x is:
y = 250(25)^x