Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

How does g(x)=10xg(x) = 10^x change over the interval from x=1x = 1 to x=3x = 3?\newlineChoices:\newline[A]g(x) increases by a factor of 20\text{[A]g(x) increases by a factor of 20}\newline[B]g(x) increases by a factor of 100\text{[B]g(x) increases by a factor of 100}\newline[C]g(x) decreases by 20%\text{[C]g(x) decreases by 20\%}\newline[D]g(x) decreases by a factor of 10\text{[D]g(x) decreases by a factor of 10}

Full solution

Q. How does g(x)=10xg(x) = 10^x change over the interval from x=1x = 1 to x=3x = 3?\newlineChoices:\newline[A]g(x) increases by a factor of 20\text{[A]g(x) increases by a factor of 20}\newline[B]g(x) increases by a factor of 100\text{[B]g(x) increases by a factor of 100}\newline[C]g(x) decreases by 20%\text{[C]g(x) decreases by 20\%}\newline[D]g(x) decreases by a factor of 10\text{[D]g(x) decreases by a factor of 10}
  1. Evaluate g(x)g(x) at lower bound: Evaluate g(x)g(x) at the lower bound of the interval.\newlineWe need to find the value of g(x)g(x) when x=1x = 1.\newlineCalculate g(1)=101g(1) = 10^1.
  2. Evaluate g(x)g(x) at upper bound: Evaluate g(x)g(x) at the upper bound of the interval.\newlineWe need to find the value of g(x)g(x) when x=3x = 3.\newlineCalculate g(3)=103g(3) = 10^3.
  3. Determine direction of change: Determine the direction of change in g(x)g(x) over the interval.\newlineCompare g(1)g(1) and g(3)g(3) to see if g(x)g(x) increases or decreases.\newlineSince 10310^3 is greater than 10110^1, g(x)g(x) increases from x=1x = 1 to x=3x = 3.
  4. Calculate growth factor: Calculate the factor by which g(x)g(x) increases over the interval.\newlineDivide g(3)g(3) by g(1)g(1) to find the growth factor.\newlineCalculate the growth factor as 103/101=1031=102=10010^3 / 10^1 = 10^{3-1} = 10^2 = 100.
  5. Match growth factor with choices: Match the calculated growth factor with the given choices.\newlineThe growth factor is 100100, so g(x)g(x) increases by a factor of 100100 from x=1x = 1 to x=3x = 3.

More problems from Describe linear and exponential growth and decay