Question

Can someone answer this question for me please ???

Answer 1

Answer:No, I do not agree with Tyler's conclusion that 5x² will always take larger values than 2x for the same value of x.

Let's analyze the table Tyler completed:

For x = 1:

5x² = 5(1)² = 5(1) = 5

2x = 2(1) = 2

For x = 2:

5x² = 5(2)² = 5(4) = 20

2x = 2(2) = 4

For x = 3:

5x² = 5(3)² = 5(9) = 45

2x = 2(3) = 6

For x = 4:

5x² = 5(4)² = 5(16) = 80

2x = 2(4) = 8

For x = 5:

5x² = 5(5)² = 5(25) = 125

2x = 2(5) = 10

From the table, we can see that for some values of x, the expression 5x² does indeed have larger values than 2x. However, this is not always the case. For example, when x = 2, 2x = 4 is larger than 5x² = 20.

The relationship between the two expressions depends on the specific value of x. In general, for values of x greater than or equal to 2, 5x² will be larger than 2x. However, for values of x less than 2, 2x will be larger than 5x².

Therefore, we cannot conclude that 5x² will always take larger values than 2x for the same value of x. The relationship between the two expressions depends on the specific value of x.

Explanation:

Answer 2

Tyler's conclusion is inaccurate. While 5x^2 may initially be larger for smaller x, 2^x eventually surpasses it due to exponential growth.

Tyler's conclusion is incorrect. Let's analyze the expressions 5x^2 and 2^x to understand their behavior for different values of x.

For 5x^2, the values increase quadratically with x. For example, when x is 1, 5x^2 is 5; when x is 2, 5x^2 is 20; and so on. The values grow rapidly as x increases due to the quadratic term.

On the other hand, for 2^x, the values increase exponentially. As x increases, 2^x grows at an increasing rate. For instance, when x is 1, 2^x is 2; when x is 2, 2^x is 4; and so forth. Exponential growth leads to a rapid increase in values as x becomes larger.

To compare the two expressions, it's important to note that the growth rate of 2^x eventually surpasses the growth rate of 5x^2. This happens because exponential growth accelerates as x increases, while quadratic growth remains relatively slower.

In summary, Tyler's conclusion is incorrect. Although 5x^2 may initially produce larger values for smaller x, the exponential growth of 2^x causes it to overtake 5x^2 as x becomes larger.