Question

1. your starting annual salary of $35,000 increases by 4% each year.
2. an item costs $4.50, and its price increases by 3.5% each year.

Explanation:

Since the problem isn't fully stated (it seems like we need to model the growth, maybe find the value after a certain number of years, but the number of years is missing), I'll assume we need to write the exponential growth formula for each. Let's handle each sub - question:

Sub - question 10 (Salary growth)

Exponential growth formula is $A = P(1 + r)^t$, where $A$ is the amount after $t$ time periods, $P$ is the initial amount, $r$ is the rate of growth per time period, and $t$ is the number of time periods.

Step 1: Identify the values

Here, the initial salary $P=\$35000$, the growth rate $r = 4\%=0.04$, and $t$ is the number of years.

Step 2: Write the formula for the salary

Substituting the values into the exponential growth formula, we get $A = 35000(1 + 0.04)^t=35000(1.04)^t$.

Sub - question 12 (Item price growth)

We use the same exponential growth formula $A = P(1 + r)^t$.

Step 1: Identify the values

The initial price $P = \$4.50$, the growth rate $r=3.5\% = 0.035$, and $t$ is the number of years.

Step 2: Write the formula for the price

Substituting the values into the formula, we get $A=4.50(1 + 0.035)^t=4.50(1.035)^t$.

If you want to find the value after a specific number of years (for example, $t = n$), you can substitute $n$ into the respective formulas. For example, if $t = 5$ for sub - question 10:

for finding value at $t = 5$ (sub - question 10)

Step 1: Substitute $t = 5$ into the salary formula

We have $A = 35000(1.04)^5$.

Step 2: Calculate $(1.04)^5$

$(1.04)^5\approx1.2166529024$.

Step 3: Calculate the salary

$A=35000\times1.2166529024\approx42582.85$.

For sub - question 12, if $t = 5$:

Answer:

for finding value at $t = 5$ (sub - question 12)

Step 1: Substitute $t = 5$ into the price formula

$A = 4.50(1.035)^5$.

Step 2: Calculate $(1.035)^5$

$(1.035)^5\approx1.1876863057$.

Step 3: Calculate the price

$A = 4.50\times1.1876863057\approx5.34458837565\approx5.34$.

Since the original problem didn't specify what to calculate, these are the general formulas and examples of calculations for a specific time period.