The graph of the function f(x)=2^x/a passes through the points (0,b) and (2,0.8). Calculate the values of a and b.

Thank you so much for huge help:)))

Substitute the pints to the function:

at (0,b):
f(x) = 2^x / a
b = 2^0 / a
b = 1/a

at (2,0.8):
f(x) = 2^x / a
0.8 = 2^2 / a
0.8 = 4 / a
a = 4 / 0.8
a = 5

Substituting to the equation for b,
b = 1/a
b = 1/5

Hope this helps :3

To find the values of a and b, we need to substitute the given coordinates into the equation f(x) = 2^x / a.

Step 1: Substituting the point (0, b) into the equation:
At x = 0, we have f(0) = 2^0 / a = 1 / a, which is equal to b. Therefore, we have the equation 1 / a = b.

Step 2: Substituting the point (2, 0.8) into the equation:
At x = 2, we have f(2) = 2^2 / a = 4 / a, which is equal to 0.8. Therefore, we have the equation 4 / a = 0.8.

Now we have a system of equations:
1 / a = b, and
4 / a = 0.8.

To solve this system, we can use either substitution or elimination method. Let's use the elimination method.

Multiply the first equation by 4 to eliminate the fractions:
4/a = b (equation 1)
4/a * 4 = b * 4
16/a = 4b

Now, we have the following two equations:
16 / a = 4b (equation 2)
4 / a = 0.8 (equation 3)

Since equation 3 is already solved for a (a = 4 / 0.8), we can substitute this value into equation 2:

16 / (4 / 0.8) = 4b

Now, simplify the equation:

16 * 0.8 / 4 = 4b
3.2 = 4b
b = 3.2 / 4
b = 0.8

Now that we have determined the value of b, we can substitute it into equation 1 to solve for a:

1 / a = 0.8
a = 1 / 0.8
a = 1.25

Therefore, the values of a and b are a = 1.25 and b = 0.8, respectively.