Question

asked Mar 4, 2024 191k views

1 Answer

Exacerbatedexpert · Answer 1 · 2024-03-09T12:07:29+0000

Answer:

$\textsf{2)} \quad f(x)=5 (2)^x$

$\textsf{3)} \quad f(x)=4 \left((1)/(2)\right)^x$

Explanation:

The general formula for an exponential function is:

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

where:

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

The end behaviours of the function are:

The y-intercept is (0, 5), so a = 5.

Another point on the curve is (1, 10).

Substitute a = 5 and point (1, 10) into the formula and solve for b:

$\implies y=ab^x$

$\implies 10=5 \cdot b^1$

$\implies 10=5 \cdot b$

$\implies b =2$

Therefore, the equation of the exponential function is:

f(x)=5 (2)^x

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

The end behaviours of the function are:

The y-intercept is (0, 4), so a = 4.

Another point on the curve is (2, 1).

Substitute a = 4 and point (2, 1) into the formula and solve for b:

$\implies y=ab^x$

$\implies 1=4 \cdot b^(2)$

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

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

Therefore, the equation of the exponential function is:

$f(x)=4 \left((1)/(2)\right)^x$

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