Question
write an exponential equation that passes through 0,1 and 1,0.1 using the y=_^x
Answers
GPT 3.5
The general form of an exponential function is y = a*b^x, where "a" and "b" are constants. Given that the function passes through the points (0, 1) and (1, 0.1), we can plug these values into the equation to find the specific values of "a" and "b".
1. When x = 0, y = 1:
1 = a*b^0
1 = a*1
a = 1
2. When x = 1, y = 0.1:
0.1 = 1*b^1
0.1 = b
b = 0.1
Therefore, the exponential equation that passes through the points (0, 1) and (1, 0.1) is:
y = (0.1)^x
1. When x = 0, y = 1:
1 = a*b^0
1 = a*1
a = 1
2. When x = 1, y = 0.1:
0.1 = 1*b^1
0.1 = b
b = 0.1
Therefore, the exponential equation that passes through the points (0, 1) and (1, 0.1) is:
y = (0.1)^x