Please HELP ASAP 31 points on

Mathematics

1 answer:

nlexa [21]2 years ago

4 0

Answer:

It's way too small and I can't read it...

Step-by-step explanation:

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For the graphed exponential equation, calculate the average rate of change from x = −3 to x = 0.

iragen [17]

Answer:

$-\frac{7}{3}$

Step-by-step explanation:

To solve this, we are using the average rate of change formula:

$m=\frac{f(b)-f(a)}{b-a}$

where

$m$ is the average rate of change

$a$ is the first point

$b$ is the second point

$f(a)$ is the function evaluated at the first point

$f(b)$ is the function evaluated at the second point

We want to know the average rate of change of the function $f(x)=0.5^x-6$ form x = -3 to x = 0, so our first point is -3 and our second point is 0. In other words, $a=-3$ and $b=0$ .

Replacing values

$m=\frac{f(b)-f(a)}{b-a}$

$m=\frac{0.5^0-6-(0.5^{-3}-6)}{0-(-3)}$

$m=\frac{1-6-(8-6)}{3}$

$m=\frac{-5-(2)}{3}$

$m=\frac{-5-2}{3}$

$m=\frac{-7}{3}$

$m=-\frac{7}{3}$

We can conclude that the average rate of change of the exponential equation form x = -3 to x = 0 is $-\frac{7}{3}$

4 0

2 years ago

Betty invests $45,000 into a cd which has an interest rate of 6.3% that compounds monthly for a total of 5 years. how much will

Lelechka [254]

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45000\\ r=rate\to 6.3\%\to \frac{6.3}{100}\dotfill &0.063\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases} \\\\\\ A=45000\left(1+\frac{0.063}{12}\right)^{12\cdot 5}\implies A=45000(1.00525)^{60}\implies A\approx 61611$