Question

use the table to answer the question.
this table
shows value
of f(x) for
different x in
an exponential
function.

x	f(x)
1	2,625
2	2,756.25
3	2,894.06

find the exponential function $f(x)=a\cdot b^x$ represented by the table

Explanation:

Step1: Find $a$ using $x=0$

For $f(x)=a\cdot b^x$, when $x=0$, $b^0=1$. So:
$$f(0)=a\cdot 1=2500 \implies a=2500$$

Step2: Calculate growth factor $b$

Use $x=1$, $f(1)=2625$ and $a=2500$:
$$b=\frac{f(1)}{a}=\frac{2625}{2500}=1.05$$

Step3: Verify $b$ with $x=2$

Check consistency:
$$f(2)=2500\cdot (1.05)^2=2500\cdot 1.1025=2756.25$$
This matches the table value.

Answer:

$f(x)=2500\cdot(1.05)^x$