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puteri [66]
3 years ago
11

The population of a parish is growing with an annual percentage rate compounded continuously. The population reaches 1.1 times i

ts previous size in 2 years.
Write the formula to find the annual percentage rate according to the exponential growth function.
Mathematics
2 answers:
Naddika [18.5K]3 years ago
8 0

Answer:

Step-by-step explanation:

The formula for continuous compounding is expressed as

A = Pe(r x t)

Where

A represents the population after t years.

P represents the initial population.

r represents the rate of growth

t represents the time in years.

From the information given,

A = 1.1 × P = 1.1P

t = 2 years

Therefore,

1.1P = Pe(r x 2)

1.1P/P = e(r x 2)

1.1 = e(2r)

Taking ln of both sides of the equation, it becomes

Ln 1.1 = 2rlne

0.095 = 2r

r = 0.095/2

r = 0.0475

Therefore, the formula to find the annual percentage rate is

A = Pe(0.0475t)

Sauron [17]3 years ago
7 0

Answer:

4.8%

Step-by-step explanation:

The population that grows with an annual percentage rate compounded continuously is given by: H = H° e^rt

Let the population be represented by H

The population reaches 1.1 times its previous size in 2 years.

So when t=2,

H = 1.1 H°

We substitute to obtain:

1.1 H° = H° e^r2

1.1 = e^2r

Take natural log to get:

In 1.1 = 2r

r = In 1.1 /2

r = 0.0477

Therefore the annual percentage rate is 4.8%

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1.61 , 1.6245, 1.512, 1.432, 1.32456

Step-by-step explanation:

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-3/2 = -1.5 and 5/3 = 1.70

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The scale on a map is 2 centimeters= 50 kilometres.Two rivers on a map are located 9.3 centimeters apart.What is The actual dist
Yuki888 [10]

Answer:

The actual distance between the two rivers is <u>232.5 kilometers</u>.

Step-by-step explanation:

GIven:

The scale on a map is 2 centimeters= 50 kilometres.Two rivers on a map are located 9.3 centimeters apart.

Now, to find the actual distance between the two rivers.

Let the actual distance between the two rivers is x.

The two rivers on the map is located apart of 9.3 centimeters.

According to the scale on the map is 2 centimeters = 50 kilometers.

<em>So, 2 centimeters is equivalent to 50 kilometers.</em>

<em>Thus, 9.3 centimeters is equivalent to </em>x.<em />

Now, to solve by using cross multiplication method:

\frac{2}{50} =\frac{9.3}{x}

<em>By cross multiplying we get:</em>

<em />2x=465<em />

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Therefore, the actual distance between the two rivers is 232.5 kilometers.

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