Question
Find the equation of the exponential function represented by the table below:
xx yy
00 0, point, 10.1
11 0, point, 30.3
22 0, point, 90.9
33 2, point, 72.7
xx yy
00 0, point, 10.1
11 0, point, 30.3
22 0, point, 90.9
33 2, point, 72.7
Answers
GPT 3.5
To find the equation of the exponential function represented by the table, we need to find the values of a and b in the equation y = ab^x.
Using the given table, we can form the equations:
0.1 = ab^0
0.3 = ab^1
0.9 = ab^2
2.7 = ab^3
From the first equation, we get ab^0 = 0.1, which simplifies to a = 0.1.
Now, we can substitute this value of a into the other equations to find b:
0.3 = 0.1b^1
0.9 = 0.1b^2
2.7 = 0.1b^3
From the second equation, we get 0.1b = 0.3, which simplifies to b = 0.3/0.1 = 3.
Substituting this value of b into the third equation, we get 0.9 = 0.1(3)^2, which simplifies to 0.9 = 0.9.
Similarly, substituting b into the fourth equation, we get 2.7 = 0.1(3)^3, which simplifies to 2.7 = 2.7.
Since all the equations are satisfied, the value of a and b are a = 0.1 and b = 3.
Therefore, the equation of the exponential function represented by the table is y = 0.1(3^x).
Using the given table, we can form the equations:
0.1 = ab^0
0.3 = ab^1
0.9 = ab^2
2.7 = ab^3
From the first equation, we get ab^0 = 0.1, which simplifies to a = 0.1.
Now, we can substitute this value of a into the other equations to find b:
0.3 = 0.1b^1
0.9 = 0.1b^2
2.7 = 0.1b^3
From the second equation, we get 0.1b = 0.3, which simplifies to b = 0.3/0.1 = 3.
Substituting this value of b into the third equation, we get 0.9 = 0.1(3)^2, which simplifies to 0.9 = 0.9.
Similarly, substituting b into the fourth equation, we get 2.7 = 0.1(3)^3, which simplifies to 2.7 = 2.7.
Since all the equations are satisfied, the value of a and b are a = 0.1 and b = 3.
Therefore, the equation of the exponential function represented by the table is y = 0.1(3^x).