Question

NO LINKS!!! URGENT HELP PLEASE!!!

Please help me with #1 and 3

Answer 1

`\textsf{1)} \quad f(x)=3 \left((1)/(2)\right)^x`

`\textsf{3)} \quad f(x)=2 (3)^x`

Explanation:

Exponential Function

The general formula for an exponential function is:

`\boxed{f(x)=ab^x}`

where:

• a is the initial value (y-intercept).
• b is the base (growth/decay factor) in decimal form.

Question 1

From inspection of the graph, this is a exponential decay function.

The end behaviours of the function are:

• As x → -∞, f(x) → +∞
• As x → +∞, f(x) → 0

The y-intercept is (0, 3), so a = 3.

Another point on the curve is (-2, 12).

Substitute a = 3 and point (-2, 12) into the formula and solve for b:

`\implies y=ab^x`

`\implies 12=3 \cdot b^(-2)`

`\implies 4= b^(-2)`

`\implies 4= (1)/(b^(2))`

`\implies b^2= (1)/(4)`

`\implies b= (1)/(2)`

Therefore, the equation of the exponential function is:

`f(x)=3 \left((1)/(2)\right)^x`

Question 3

From inspection of the graph, this is a exponential growth function.

The end behaviours of the function are:

• As x → -∞, f(x) → 0
• As x → +∞, f(x) → +∞

The y-intercept is (0, 2), so a = 2.

Another point on the curve is (1, 6).

Substitute a = 2 and point (1, 6) into the formula and solve for b:

`\implies y=ab^x`

`\implies 6=2 \cdot b^1`

`\implies 6=2 \cdot b`

`\implies b = 3`

Therefore, the equation of the exponential function is:

`f(x)=2 (3)^x`