which value of a in the exponential function below would cause the function to shrink?\n$f(x)=a(\\frac{3}{2})…

which value of a in the exponential function below would cause the function to shrink?\n$f(x)=a(\\frac{3}{2})^x$\n$\\frac{4}{5}$\n$\\frac{5}{4}$\n$\\frac{3}{2}$\n$\\frac{7}{4}$

which value of a in the exponential function below would cause the function to shrink?\n$f(x)=a(\\frac{3}{2})^x$\n$\\frac{4}{5}$\n$\\frac{5}{4}$\n$\\frac{3}{2}$\n$\\frac{7}{4}$

Answer

Explanation:

Step1: Recall exponential - function transformation rule

For an exponential function (y = a\cdot b^{x}), if (|a|< 1), the function shrinks vertically compared to (y = b^{x}).

Step2: Compare each option with 1

  • Option 1: (\frac{4}{5}=0.8<1).
  • Option 2: (\frac{5}{4} = 1.25>1).
  • Option 3: (\frac{3}{2}=1.5>1).
  • Option 4: (\frac{7}{4}=1.75>1).

Answer:

A. (\frac{4}{5})