Question

NO LINKS!! Help me please​

Answer 1

`y=7 (1.5)^x`

Explanation:

General form of an exponential function:
`y=ab^x`

where:

• 
  `a` is the y-intercept (or initial value)
• 
  `b` is the base (or growth factor)
• 
  `x` is the independent variable

If
`b > 1` then it is an increasing function

If
`0 < b < 1` then it is a decreasing function

Given:

• (1, 10.5)
• (3, 23.625)

Substitute these ordered pairs into the general form of the exponential function:

Equation 1:
`ab^1=10.5`

Equation 2:
`ab^3=23.625`

To find
`b`, divide Equation 2 by Equation 1:

`\implies (ab^3)/(ab^1)=(23.625)/(10.5)`

`\implies b^2=2.25`

`\implies b=√(2.25)`

`\implies b=1.5`

Now substitute found value of
`b` into one of the equations to find
`a`:

`\implies ab=10.5`

`\implies 1.5a=10.5`

`\implies a=(10.5)/(1.5)`

`\implies a=7`

Therefore, the final exponential equation is:
`y=7 (1.5)^x`

Answer 2

y = 7·1.5^x

Explanation:

To find the parameters of the exponential function, substitute the given point values and solve the resulting equations for the parameters.

The form you want to find the parameters of is ...

y = ab^x

__

For (x, y) = (1, 10.5)

10.5 = ab^1

For (x, y) = (3, 23.625)

23.625 = ab^3

__

The value of 'b' can be found by dividing the second equation by the first:

`(23.625)/(10.5)=(ab^3)/(ab^1)\\\\2.25 = b^2\\\\b=√(2.25)=1.5`

Then the value of 'a' can be found by substituting for b in the first equation:

10.5 = a(1.5^1)

a = 10.5/1.5 = 7

The exponential function is ...

y = 7·1.5^x