Question

(Q8) The graph of an exponential function is given. Which of the following is the correct equation of the function? (Picture Provided)

Answer 1

Answer:

b. $y=3.9^x$

Step-by-step explanation:

Remember that the standard exponential function is $y=ab^x$

where

$a$ is the coefficient

$b$ is the base

If $b>0$, the function is growing

If $0<b<1$ the graph is decaying

We can infer from the graph that the function is growing, so we can discard $y=0.45^x$ and $y=0.73^x$.

Now, to evaluate our tow remaining equations, we are using the test values $x=0$ and $x=1$:

For $y=1.8^x$

For $x=0$

$y=1.8^0$

$y=0$

For $x=1$

$y=1.8^1$

$y=1.8$

The graph passes through the points (0,1) and (1, 1.8)

For $y=3.9^x$

$x=0$

$y=3.9^0$

$y=0$

$x=1$

$y=3.9^1$

$y=3.9$

The graph passes through the points (0,1) and (1, 3.9)

We can see in the graph when $x=1$, $y$ is almost 4, so we can conclude that the correct equation is $y=3.9^x$