question 12(multiple choice worth 6 points)\n(semi - log plots lc)\ndetermine the linear rate of change and…

question 12(multiple choice worth 6 points)\n(semi - log plots lc)\ndetermine the linear rate of change and the initial value of the corresponding linear form of the exponential function g(x)=0.86·2.35^x.\nthe linear rate of change is log₂.₃₅ 10, and the initial value is log₀.₈₆ 10.\nthe linear rate of change is log₀.₈₆ 10, and the initial value is log₂.₃₅ 10.\nthe linear rate of change is log 2.35, and the initial value is log 0.86.\nthe linear rate of change is log 0.86, and the initial value is log 2.35.

question 12(multiple choice worth 6 points)\n(semi - log plots lc)\ndetermine the linear rate of change and the initial value of the corresponding linear form of the exponential function g(x)=0.86·2.35^x.\nthe linear rate of change is log₂.₃₅ 10, and the initial value is log₀.₈₆ 10.\nthe linear rate of change is log₀.₈₆ 10, and the initial value is log₂.₃₅ 10.\nthe linear rate of change is log 2.35, and the initial value is log 0.86.\nthe linear rate of change is log 0.86, and the initial value is log 2.35.

Answer

Explanation:

Step1: Recall exponential - linear conversion

For an exponential function $y = a\cdot b^{x}$, taking the common logarithm of both sides gives $\log y=\log a + x\log b$. In the form $Y = mx + c$ (linear form), where $Y=\log y$, $m$ is the slope (linear rate of change) and $c$ is the $Y -$intercept (initial value in the linear form). For the function $g(x)=0.86\cdot2.35^{x}$, taking the common logarithm: $\log(g(x))=\log(0.86)+x\log(2.35)$.

Step2: Identify linear rate of change and initial value

The linear rate of change (slope of the linear - form function) is $\log(2.35)$ and the initial value (value of the linear - form function when $x = 0$) is $\log(0.86)$.

Answer:

The linear rate of change is $\log 2.35$, and the initial value is $\log 0.86$. So the correct option is: The linear rate of change is $\log 2.35$, and the initial value is $\log 0.86$.