Lesson 1 Practice Problems 1. Which expression equals 2^7 A. 2+2+2+2+2+2+2 B. 2cdot 2cdot 2cdot 2cdot 2cdot 2cdot 2 C. 2cdot 7 D. 2+7 2. Evaluate the expression 3cdot 5^x when x is 2. 3. The graph shows the yearly balance, in dollars, in an investment account. a. What is the initial balance in the account? b. Is the account growing by the same number of dollars each year? Explain how you know. C. A second investment account starts with 2,000 and grows by 150 each year. Sketch the values of this account on the graph. d. How does the growth of balances in the two account balances compare?

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Lesson 1 Practice Problems 1. Which expression equals 2^7 A. 2+2+2+2+2+2+2 B. 2cdot 2cdot 2cdot 2cdot 2cdot 2cdot 2 C. 2cdot 7 D. 2+7 2. Evaluate the expression 3cdot 5^x when x is 2. 3. The graph shows the yearly balance, in dollars, in an investment account. a. What is the initial balance in the account? b. Is the account growing by the same number of dollars each year? Explain how you know. C. A second investment account starts with 2,000 and grows by 150 each year. Sketch the values of this account on the graph. d. How does the growth of balances in the two account balances compare?

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Let's address each question step by step.1. Which expression equals $2^{7}$ ?To solve this, we need to understand what $2^{7}$ means. It means 2 multiplied by itself 7 times.A. $2+2+2+2+2+2+2$ - This is 2 added to itself 7 times, not multiplied.B. $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$ - This is 2 multiplied by itself 7 times, which is the correct interpretation of $2^{7}$.C. $2 \cdot 7$ - This is just 2 multiplied by 7, which is 14.D. $2+7$ - This is just 2 added to 7, which is 9.Answer: B. $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$2. Evaluate the expression $3 \cdot 5^{x}$ when $x$ is 2.To evaluate this expression, we substitute 2 for $x$ and calculate:$3 \cdot 5^{2} = 3 \cdot (5 \cdot 5) = 3 \cdot 25 = 75$Answer: 753. The graph shows the yearly balance, in dollars, in an investment account.a. What is the initial balance in the account?The initial balance is the amount at year 0, which is given as (0, 1000).Answer: The initial balance is $1000.b. Is the account growing by the same number of dollars each year? Explain how you know.To determine if the account is growing by the same amount each year, we look at the differences in the balance from year to year.From year 0 to 1:$1100 - $1000 =$100From year 1 to 2: $1400 -$1100 = $300From year 2 to 3:$1500 - $1400 =$100... and so on.The differences are not consistent, which means the account is not growing by the same number of dollars each year.Answer: No, the account is not growing by the same number of dollars each year because the differences in the yearly balances are not consistent.c. A second investment account starts with $\$ 2,000$ and grows by $\$ 150$ each year. Sketch the values of this account on the graph.To sketch the values of this account on the graph, we would start at $2000 at year 0 and add$150 for each subsequent year.Year 0: $2000Year 1:$2000 + $150 =$2150Year 2: $2150 +$150 = $2300... and so on.This would create a straight line with a constant slope on the graph.Answer: (This part requires a visual representation which cannot be provided in text format, but the values for each year can be calculated as shown.)d. How does the growth of balances in the two account balances compare?The first account does not grow by a consistent amount each year; it grows by different amounts, which suggests a variable interest rate or different deposits/withdrawals. The second account grows by a consistent$150 each year, which suggests a fixed interest rate or consistent annual deposit.Answer: The first account has variable growth, while the second account grows by a consistent amount each year.

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