Question

Exponential function that go through points (0,10) and (3,7290)

Answer 1

To find the exponential function that goes through the points (0,10) and (3,7290), we can solve for the initial value and growth/decay factor. The exponential function is y = 10 * 9^x.

Step-by-step explanation:

To find the exponential function that goes through the points (0,10) and (3,7290), we can start by writing an equation in the form of y = ab^x, where a is the initial value and b is the growth/decay factor. Using the first point (0,10), we have 10 = ab^0, which simplifies to a = 10. Now, using the second point (3,7290), we have 7290 = 10 * b^3. Dividing both sides by 10, we get b^3 = 729, and taking the cube root of both sides, we find b = 9. Therefore, the exponential function that goes through the given points is y = 10 * 9^x.

Answer 2

The exponential function that go through points (0,10) and (3,7290) is:

`y = 10*9^x`

How to find the exponential function?

A general exponential function is written as:

`y = A*b^x`

Where A is the initial value and b is the rate of growth/decay.

Here we know that we have the point (0, 10), replacing these values in the equation we get:

`10 = A*b^0\\10 = A`

Then we have:

`y = 10*b^x`

And we also have (3, 7290), replacing these values we get:

`7290 = 10*b^3\\7290/10 = b^3\\729 = b^3\\\sqrt[3]{729} = b\\9 = b`

So the exponential equation is:

`y = 10*9^x`