Question

without graphing, describe the shape of the graph of the function. find the second coordinates of the points with first coordinates 0 and 1.
$f(x)=2.9^x$
the graph exponentially grows.
find the second coordinates of the given first coordinates.
$\

$$\begin{array}{|c|c|c|}\\hline x & f(x)=2.9^x \\\\ \\hline 0 & f(0)=\\square \\\\ \\hline 1 & f(1)=\\square \\\\ \\hline \\end{array}$$

$
(round to one decimal place as needed.)

Explanation:

Step1: Calculate f(0)

$f(0)=2.9^0 = 1$

Step2: Calculate f(1)

$f(1)=2.9^1 = 2.9$

Step3: Describe the graph shape

This is an exponential growth function with base $2.9>1$, so it starts at the point $(0,1)$, increases slowly at first, then grows more rapidly as $x$ increases, and approaches 0 as $x$ approaches negative infinity.

Answer:

• The graph is an exponential growth curve: it approaches 0 as $x\to-\infty$, passes through $(0,1)$, and increases rapidly as $x$ increases.
• $f(0)=1$
• $f(1)=2.9$