Question

How do you solve this pls

Answer 1

Step-by-step explanation:

The equation of a exponential function is

$a \times (b) {}^{x}$

where a is the y value of the y intercept, b is the constant rate of change.

Here the y intercept is (0,4), the y value of the y intercept is 4.

So a=4

The graph passes through point (1,2) so

$h(x) = 4 \times b {}^{x}$

Plug in 1 for x, 2 for h(x)

$2 = 4 \times {b}^{1}$

Anything to the first power is itself so

$2 = 4 \times b$

Isolate b.

$\frac{1}{2} = b$

So our function is

$4 \times ( \frac{1}{2} ) {}^{x}$

Answer 2

Answer:

$h(x)=4\left(\dfrac{1}{2}\right)^x$

Step-by-step explanation:

Exponential Function

General form of an exponential function: $f(x)=ab^x$

where:

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

From inspection of the given diagram, the defined points on the curve are:

• (0, 4)
• (1, 2)

As one of the defined points is the y-intercept:

$\implies a=4$

Substitute the found value of a and the point (1, 2) into the general form of an exponential function and solve for b:

$\begin{aligned}h(x)=ab^x & \\\implies h(1)=4b^1 & = 2\\4b & = 2\\b & = \dfrac{2}{4}\\b & =\dfrac{1}{2} \end{aligned}$

Finally, substitute the found values of a and b to complete the equation for h(x):

$\implies h(x)=4\left(\dfrac{1}{2}\right)^x$

Learn more about exponential functions:

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