Which term is described by a function that grows with a constant ratio?

Which term is described by a function that grows with a constant ratio?

• A. Quadratic
• B. Logarithmic function
• C. Reusability
• D. Exponential function

Answer: (D)

Constant-ratio growth is a hallmark of exponential functions. If you have a function like y = a · b^x, increasing x by 1 multiplies the output by the same amount b, so the ratio y(x+1)/y(x) stays constant. That fixed multiplier is what defines exponential growth. Quadratic growth follows x^2, where the successive ratios aren’t constant—the growth speeds up as x increases. Logarithmic growth rises quickly at first and then levels off, so its consecutive-value ratios change. Reusability isn’t describing a growth pattern of a function. So the term that matches growth with a constant ratio is the exponential function.

Constant-ratio growth is a hallmark of exponential functions. If you have a function like y = a · b^x, increasing x by 1 multiplies the output by the same amount b, so the ratio y(x+1)/y(x) stays constant. That fixed multiplier is what defines exponential growth.

Quadratic growth follows x^2, where the successive ratios aren’t constant—the growth speeds up as x increases. Logarithmic growth rises quickly at first and then levels off, so its consecutive-value ratios change. Reusability isn’t describing a growth pattern of a function. So the term that matches growth with a constant ratio is the exponential function.