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The graph of $f(x)=10(0.75)^x$ for $x\geq0$ is shown. What is the initial value of the function?

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Linear approximation

Full solution

Q. The graph of

f(x)=10(0.75)^x

for

x\geq0

is shown. What is the initial value of the function?

Evaluate $f(0)$ : The initial value of a function is the value of the function when $x$ is $0$ . To find the initial value of the function $f(x)=10(0.75)^x$ , we need to evaluate $f(0)$ .
Substitute $x$ with $0$ : Substitute $x$ with $0$ in the function $f(x)=10(0.75)^x$ to calculate the initial value. $\newline$ $f(0)=10(0.75)^0$
Calculate $(0.75)^0$ : Any non-zero number raised to the power of $0$ is $1$ . Therefore, $(0.75)^0$ is $1$ . $10(0.75)^0 = 10 \times 1$
Multiply $10$ by $1$ : Multiply $10$ by $1$ to get the initial value. $\newline$ $10 \times 1 = 10$

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