The general form of an exponential function is y = ab^x.

We know that the function passes through the points (0,16) and (5,512).

We can use these points to form two equations and solve for the values of a and b.

From the point (0,16), we substitute x = 0 and y = 16 into the equation to get:

16 = ab^0
Since any number to the power of 0 is 1, we get a = 16.

Now we know the value of a, we can use the second point (5,512) to find the value of b. We substitute x = 5, y = 512 and a = 16 into the equation to get:

512 = 16b^5
Divide both sides by 16 to get:
32 = b^5
Take the fifth root of both sides to get:
b = 2

So, the exponential function that passes through the points (0,16) and (5,512) is y = 16*2^x.

Question

The general form of an exponential function is y = ab^x.

We know that the function passes through the points (0,16) and (5,512).

We can use these points to form two equations and solve for the values of a and b.

From the point (0,16), we substitute x = 0 and y = 16 into the equation to get:

16 = ab^0
Since any number to the power of 0 is 1, we get a = 16.

Now we know the value of a, we can use the second point (5,512) to find the value of b. We substitute x = 5, y = 512 and a = 16 into the equation to get:

512 = 16b^5
Divide both sides by 16 to get:
32 = b^5
Take the fifth root of both sides to get:
b = 2

So, the exponential function that passes through the points (0,16) and (5,512) is y = 16*2^x.

Knowee AI · Accepted Answer

The general form of an exponential function is y = ab^x.

We know that the function passes through the points (0,16) and (5,512).

We can use these points to form two equations and solve for the values of a and b.

From the point (0,16), we substitute x = 0 and y = 16 into the equation to get:

16 = ab^0
Since any number to the power of 0 is 1, we get a = 16.

Now we know the value of a, we can use the second point (5,512) to find the value of b. We substitute x = 5, y = 512 and a = 16 into the equation to get:

512 = 16b^5
Divide both sides by 16 to get:
32 = b^5
Take the fifth root of both sides to get:
b = 2

So, the exponential function that passes through the points (0,16) and (5,512) is y = 16*2^x.

Write an exponential function in the form y, equals, a, b, to the power xy=ab x that goes through the points left parenthesis, 0, comma, 16, right parenthesis(0,16) and left parenthesis, 5, comma, 512, right parenthesis(5,512).

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