Mathematics: Which set of steps shows the solution to the equation 2y = −8? y = −8 − 2; y = 6 y = −8 ÷ (−2); y = 4 y = −8 ÷ 2; y = −4 y = −8 − (−2); y = −6

Which set of steps shows the solution to the equation

iiChantxx

02.01.2022

The correct option is

Step-by-step explanation: We are given to select the correct steps that shows the solution to the following equation :

2y=-8~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

We know that

the solution to the equation $ax=b,~~\textup{a,b are real numbers}$ is given by

$ax=b\\\\\Rightarrow x=b\div a.$

Therefore, the solution of equation (i) is as follows :

$2y=-8\\\\\Rightarrow y=-8\div 2\\\\\Rightarrow y=\dfrac{-8}{2}\\\\\Rightarrow y=-4.$

Thus, (C) is the correct option.

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wwwcarolynzouowficz

15.10.2022

(See explanation)

Step-by-step explanation:

The differential equation for a exponential growth is:

$\frac{dn}{dt} = k\cdot n$

The formula is rearranged and integrated afterwards:

$\frac{dn}{n} = k \cdot dt$

$\int\limits_{n_{o}}^{n} {\frac{dn}{n} } = k\cdot \int\limits_{0}^{t}\, dt$

$\ln \frac{n}{n_{o}} = k\cdot t$

$\frac{n}{n_{o}} = e^{ k\cdot t}$

$n = n_{o}\cdot e^{k\cdot t}$

The exponential growth function can be used to find the montly growth function as follows:

$\ln 1.2 = k\cdot 12$

k = 0.015

The coeffcients of the expression are, respectively:

$n_{o} = 25$

k = 0.015

The exponential growth function with a monthly growth rate is:

$n(t) = 25\cdot e^{0.015\cdot t}$ , where t is measured in months.

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