Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

In the following expression, both AA and BB are variables that can take positive values.\newlineA(B)(B+2)A^{(B)}(B+2)\newlineWhich of these actions will cause the expression's value to increase?\newlineChoose 22 answers:\newlineA). Keeping AA constant and increasing BB\newlineB). Keeping AA constant and decreasing BB\newlineC). Increasing AA and keeping BB constant\newlineD). Decreasing AA and keeping BB constant

Full solution

Q. In the following expression, both AA and BB are variables that can take positive values.\newlineA(B)(B+2)A^{(B)}(B+2)\newlineWhich of these actions will cause the expression's value to increase?\newlineChoose 22 answers:\newlineA). Keeping AA constant and increasing BB\newlineB). Keeping AA constant and decreasing BB\newlineC). Increasing AA and keeping BB constant\newlineD). Decreasing AA and keeping BB constant
  1. Analyze Expression AB(B+2)A^{B}(B+2): First, let's analyze the expression AB(B+2)A^{B}(B+2). This expression means AA raised to the power of BB, multiplied by (B+2)(B+2). To understand how changes in AA or BB affect the expression, we need to consider how each component behaves.
  2. Option A: Increase B: Consider option A: Keeping AA constant and increasing BB. Increasing BB will increase the exponent BB in ABA^B, making ABA^B larger since A > 1. Also, (B+2)(B+2) increases as BB increases, thus the entire expression A(B)(B+2)A^{(B)}(B+2) increases.
  3. Option B: Decrease BB: Now, look at option B: Keeping AA constant and decreasing BB. Decreasing BB will decrease the exponent in ABA^B, making ABA^B smaller since A > 1. Also, (B+2)(B+2) decreases as BB decreases, thus the entire expression AB(B+2)A^{B}(B+2) decreases.
  4. Option C: Increase AA: Consider option C: Increasing AA and keeping BB constant. Increasing AA while BB remains constant will increase the value of ABA^B, as the base of the exponentiation is getting larger. Since (B+2)(B+2) remains constant, the overall expression A(B)(B+2)A^{(B)}(B+2) increases.
  5. Option D: Decrease AA: Finally, examine option D: Decreasing AA and keeping BB constant. Decreasing AA while BB remains constant will decrease the value of ABA^B, as the base of the exponentiation is getting smaller. Since (B+2)(B+2) remains constant, the overall expression A(B)(B+2)A^{(B)}(B+2) decreases.

More problems from Find the constant of variation