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3 years ago

Can someone help me with this plz I am so confused??

Mathematics

2 answers:

MAVERICK [17]3 years ago

8 0

Answer:

f = -5/3.

Step-by-step explanation:

We want to isolate f on the left side of the equation.

To do this we multiply both sides by -4/3 , because -3/4 * -4/3 = 1 giving us 1f.

-4/3 * -3/4 f = 5/4 * -4/3

-12/-12 f = 5/4 * -4/3

1 f = -20/12

f = - 5/3.

ruslelena [56]3 years ago

6 0

F= -1 2/3 or 5/3

In order to find the answer all you have to do is multiply both sides by -4/3.

-3/4f × -4/3 = f

-4/3 × 5/4 = -20/12

-20/12 simplified is -5/3 or -1 2/3

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d) The population when t = 5, N(5) = 697 = 700( to the nearest 50)

Step-by-step explanation:

The rate of change of N(t) can be written as dN/dt

According to the question, $\frac{dN}{dt} \alpha (725 - N(t))$

$\frac{dN}{dt} = k (725 - N)\\\frac{dN}{725 - N} = kdt$

Integrating both sides of the equation

$\int {\frac{1 }{725 - N}} \, dN = \int {k} \, dt\\- ln (725 - N) = kt + C\\ ln (725 - N) = -(kt + C)\\725 - N = e^{-(kt + C)} \\725 - N = e^{-kt} * e^{-C} \\725 - N = C e^{-kt}\\N = 725 - C e^{-kt}$

When t = 0, N = 400

$400 = 725 - C e^{-k*0}\\400 = 725 - C\\C = 725 - 400\\C = 325$

When t = 3, N = 650

$650 = 725 - (325 * e^{-3k})\\325 * e^{-3k} = 75\\e^{-3k} = 75/325\\e^{-3k} = 0.23\\-3k = ln 0.23\\-3k = -1.47\\k = 1.47/3\\k = 0.49$

The equation for the population becomes:

$N = 725 - 325 e^{-0.49t}$

At t = 5, the population becomes:

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