Tell whether the function represents exponential growth or exponential decay. Then graph the function.

$y={\left(1.8\right)}^{x}$

Jamya Elliott
2022-01-30
Answered

Tell whether the function represents exponential growth or exponential decay. Then graph the function.

$y={\left(1.8\right)}^{x}$

You can still ask an expert for help

plusmarcacw

Answered 2022-01-31
Author has **10** answers

The base of the function $y={1.8}^{x}is1.8>1,$

so the function represents exponential growth.

Look at the base to determine whether it is growth or decay. If the base is greater than 1, the function represents exponential growth. If the base is less than 1, the function represents exponential decay.

To sketch the graph, find a few points (x,y) by choosing some value x and calculating its pair

$y={1.8}^{x}$ , then drawa smooth curve through
those points.

exponential growth

so the function represents exponential growth.

Look at the base to determine whether it is growth or decay. If the base is greater than 1, the function represents exponential growth. If the base is less than 1, the function represents exponential decay.

To sketch the graph, find a few points (x,y) by choosing some value x and calculating its pair

exponential growth

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Need to find a solution to the following system of linear inequalities:

$\begin{array}{rl}{x}_{1}-{x}_{2}& \le 1\\ {x}_{1}-{x}_{4}& \le -4\\ {x}_{2}-{x}_{3}& \le 2\\ {x}_{2}-{x}_{5}& \le 7\\ {x}_{2}-{x}_{6}& \le 5\\ {x}_{3}-{x}_{6}& \le 10\\ {x}_{4}-{x}_{2}& \le 2\\ {x}_{5}-{x}_{1}& \le -1\\ {x}_{5}-{x}_{4}& \le 3\\ {x}_{6}-{x}_{3}& \le -8\end{array}$

Is there any systematic way to find a solution?

$\begin{array}{rl}{x}_{1}-{x}_{2}& \le 1\\ {x}_{1}-{x}_{4}& \le -4\\ {x}_{2}-{x}_{3}& \le 2\\ {x}_{2}-{x}_{5}& \le 7\\ {x}_{2}-{x}_{6}& \le 5\\ {x}_{3}-{x}_{6}& \le 10\\ {x}_{4}-{x}_{2}& \le 2\\ {x}_{5}-{x}_{1}& \le -1\\ {x}_{5}-{x}_{4}& \le 3\\ {x}_{6}-{x}_{3}& \le -8\end{array}$

Is there any systematic way to find a solution?

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$$\begin{array}{}X& f(x)\\ 0& 0\\ 2& 401\\ 4& 1598\\ 6& 3595\\ 8& 6407\\ 10& 10,009\end{array}$$

The quadratic function is y=.

(Type an equation using as the variable. Round to two decimals places as needed)

The quadratic function is y=.

(Type an equation using as the variable. Round to two decimals places as needed)

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Assume $0<r<1<p$ and $k,\lambda \ge 0$. Let the functions $y,z\in {C}^{1}(0,T)$ satisfy $y\ge 0$, $z>0$ and the system of differential inequalities

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on $(0,T)$. Then $T<\infty $ ($T$ is the maximum lifetime of the solution).

${z}^{\prime}\ge {y}^{p}$

${y}^{\prime}+\lambda y+k{z}^{\prime r}\ge z$

on $(0,T)$. Then $T<\infty $ ($T$ is the maximum lifetime of the solution).

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