Question

find the equation that models this data.
time (minutes) 0 1 2 3
height (feet) 0.5 1.5 4.5 13.5
step 1: plot the data points on the graph.
step 2: analyze the graph and determine the relationship.
the relationship is
exponential
linear
quadratic

Explanation:

Step1: Identify the general form of an exponential function

The general form of an exponential function is $y = ab^{x}$, where $a$ is the initial - value and $b$ is the base. When $x = 0$, $y=a$. From the table, when $x = 0$, $y = 0.5$, so $a=0.5$.

Step2: Find the value of the base $b$

We know that when $x = 1$, $y = 1.5$. Substitute $a = 0.5$, $x = 1$, and $y = 1.5$ into $y=ab^{x}$. We get $1.5=0.5b^{1}$. Solving for $b$:
\[b=\frac{1.5}{0.5}=3\]

Answer:

$y = 0.5\times3^{x}$