All categories

3 years ago

The population on an island is modeled by P(t)=600040+60e−0.03t

Mathematics

1 answer:

otez555 [7]3 years ago

4 0

Answer:

600040

Step-by-step explanation:

Given the population of people on an island modeled by the equation P(t)=600040+60e−0.03t for t≥0 where P(t) is the number of people on the island after years. To get limt→∞P(t), we will substitute infinity into the equation as shown;

limt→∞ 600040+60e−0.03t

= 600040+60e−0.03(∞)

= 600040+60e−∞

= 600040+60(1/e∞)

Note that 1/e∞ = 1/∞ = 0

Hence the equation becomes;

= 600040+60(0)

= 600040

Hence limt→∞P(t) is 600040

You might be interested in

Select the number line that correctly shows the calculation for |−3|.

Oxana [17]

It is the third answer. Absolute value just means the distance from that number (-3 in your case) to 0 on a number line. Choice 3 shows just that.

7 0

3 years ago

Read 2 more answers

If tan theta = 10/13 and cos theta > 0 then sin2theta is what ?

svetoff [14.1K]

$sin2\alpha = \frac{260}{269}$

<u>Step-by-step explanation:</u>

We have , $Tan\alpha = \frac{Perpendicular}{Base} = \frac{10}{13}$ ,

We know that $sin\alpha = \frac{Perpendicular}{Hypotenuse} = \frac{Perpendicular}{\sqrt[2]{(Perpendicualr)^{2} + (Base)^{2})} }$

Substituting values of P & B , $sin\alpha = \frac{10}{\sqrt{10^{2} + 13^{2}} } = \frac{10}{\sqrt{269} }$

Now , $sin2\alpha = 2sin\alpha cos\alpha = 2sin\alpha \sqrt{1 - (sin\alpha)^{2} }$

⇒ $sin2\alpha =$ $\frac{10}{\sqrt{269} }$ × $\sqrt{1 - (\frac{10}{\sqrt{269} })^{2} }$ ×2

⇒ $sin2\alpha = \frac{20}{\sqrt{269} }( \sqrt{\frac{269 - 100}{269} } )$

⇒ $sin2\alpha = \frac{20}{\sqrt{269} }( \sqrt{\frac{169 }{269} } )$

⇒ $sin2\alpha = \frac{260}{\sqrt{269} }( \sqrt{\frac{1}{269} } )$

⇒ $sin2\alpha = \frac{260}{269}$

6 0

3 years ago

Help please will give brainlyest

Tomtit [17]

It is a blank picture I can’t do anything

6 0

3 years ago

Read 2 more answers

A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t

xz_007 [3.2K]

Full Question

A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t = 0, the resulting mass—spring system is disturbed from its rest state by the force F (t) = 20 cos(8t). The force F (t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds.

Determine the spring constant k.

Answer:

Spring Constant = 1000Nm^-1

Step-by-step explanation:

Given

Mass = 10kg

Spring Extension = 9.8cm

Spring Constant K = Force/Extension

Force = Mass * Acceleration

Force = 10 * 9.8 = 9.8N

Spring Extension = 9.8 cm = 9.8 /100 = 0.098 m

Spring constant = 98 / 0.098

Spring Constant = 1000Nm^-1

3 0

2 years ago

Which statement regarding the function y=cos(x) is true?

MAVERICK [17]

<span>A. cos(x) = cos(-x) [correct, since cos(x) is an even function]
B. Since the cosine function is even, reflection over the x-axis [y-axis] does not change the graph. [false]
C. cos(x) = -cos(x) [ false]
D. The cosine function is odd [even], so it is symmetrical across the origin. [false]</span>

6 0

2 years ago

Read 2 more answers