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
(1 point)
$f(x) = \square \cdot \square^x$
check answer remaining attempts 3

Explanation:

Step1: Find the value of \( a \)

For an exponential function \( f(x) = a \cdot b^x \), when \( x = 0 \), \( b^0 = 1 \), so \( f(0) = a \cdot 1 = a \). From the table, when \( x = 0 \), \( f(0) = 2500 \), so \( a = 2500 \).

Step2: Find the value of \( b \)

Now we know \( a = 2500 \), so the function is \( f(x) = 2500 \cdot b^x \). Use the point \( (1, 2625) \). Substitute \( x = 1 \) and \( f(1) = 2625 \) into the function: \( 2625 = 2500 \cdot b^1 \). Solve for \( b \): \( b=\frac{2625}{2500}=1.05 \).

Step3: Write the exponential function

Now that we have \( a = 2500 \) and \( b = 1.05 \), the exponential function is \( f(x)=2500\cdot(1.05)^x \).

Answer:

\( f(x) = \boldsymbol{2500} \cdot \boldsymbol{(1.05)}^x \)