Mathematics
11.06.2022 12:53
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Solve the equation below 0.2(x-3)=2x-6

Solve the equation below 0.2(x-3)=2x-6
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Savagepanda911
Savagepanda911
4,6(35 marks)

0.2(x-3)=2x-6

x-3=10x-30

-9x=-27

x=3

aaronhid3
aaronhid3
4,5(23 marks)

(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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