Answer :

To solve the function [tex]\( f(x) = 7000(1 + 2.5)^x \)[/tex] for specific values of [tex]\( x \)[/tex], we'll go through the process of evaluating the expression:

1. Understand the Function Structure:
- The function is defined as [tex]\( f(x) = 7000 \times (1 + 2.5)^x \)[/tex].
- This function features a base value of [tex]\( 7000 \)[/tex] and a growth factor, which is [tex]\( 1 + 2.5 = 3.5 \)[/tex].

2. Evaluate for Specific Values of [tex]\( x \)[/tex]:
- We will calculate the value of [tex]\( f(x) \)[/tex] for [tex]\( x = 1 \)[/tex] and [tex]\( x = 2 \)[/tex].

3. Calculate [tex]\( f(x) \)[/tex] for [tex]\( x = 1 \)[/tex]:
- Substitute [tex]\( x = 1 \)[/tex] into the function:
[tex]\[
f(1) = 7000 \times (3.5)^1
\][/tex]
- Simplify the exponent:
[tex]\[
(3.5)^1 = 3.5
\][/tex]
- Multiply:
[tex]\[
7000 \times 3.5 = 24500
\][/tex]

4. Calculate [tex]\( f(x) \)[/tex] for [tex]\( x = 2 \)[/tex]:
- Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[
f(2) = 7000 \times (3.5)^2
\][/tex]
- Simplify the exponent:
[tex]\[
(3.5)^2 = 3.5 \times 3.5 = 12.25
\][/tex]
- Multiply:
[tex]\[
7000 \times 12.25 = 85750
\][/tex]

Therefore, the results are:
- [tex]\( f(1) = 24500 \)[/tex]
- [tex]\( f(2) = 85750 \)[/tex]

These values are what you obtain when you substitute [tex]\( x = 1 \)[/tex] and [tex]\( x = 2 \)[/tex] into the function and carry out the calculations step-by-step.

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Rewritten by : Barada