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3 years ago

14

The exponential model A = 661.7 e^0.011t describes the population, A, of a country in millions, t years after 2003. Use the mode

l to determine the population of the country in 2003

1 answer:

faust18 [17]3 years ago

7 0

Answer:

661.7 million

Step-by-step explanation:

Given the exponential model :

A = 661.7 e^0.011t

The general form of an Exponential model is expresses as :

A = A0 * e^rt

Where A = final value ; A0 = Initial value ; r = growth rate and t = time elapsed

From the question t = time after 2003

Therefore, A0 = initial population, which is the population in 2003

Therefore, A0 = 661.7

Or we could put t = 0 in the equation and solve for A

A = 661.7 e^0.011(0)

A = 661.7 * 1

A = 661.7

Hence, population in 2003 is 661.7 million

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What is the sum of series is numbers 64&66 ?<br> Using the summation notation

iragen [17]

Answer:

64. 6138

66. 8.078125

Step-by-step explanation:

Let's take it one number at a time.

For number 64:

$6(2)^{1-1}=6$

$6(2)^{2-1}=12$

$6(2)^{3-1}=24$

$6(2)^{4-1}=48$

$6(2)^{5-1}=96$

$6(2)^{6-1}=192$

$6(2)^{7-1}=384$

$6(2)^{8-1}=768$

$6(2)^{9-1}=1536$

$6(2)^{10-1}=3072$

Sum = 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 + 3072

Sum = 6138

For number 66:

$12(-\frac{1}{2})^{0}=12$

$12(-\frac{1}{2})^{1}=-6$

$12(-\frac{1}{2})^{2}=3$

$12(-\frac{1}{2})^{3}=-1.5$

$12(-\frac{1}{2})^{4}=0.75$

$12(-\frac{1}{2})^{5}=-0.375$

$12(-\frac{1}{2})^{6}=0.1875$

$12(-\frac{1}{2})^{7}=-0.0078125$

$12(-\frac{1}{2})^{8}=0.046875$

$12(-\frac{1}{2})^{9}=-0.0234375$

Sum = 12 + -6 + 3 + -1.5 + 0.75 + -0.375 + 0.1875 + -0.0078125 + 0.046875 + -0.0234375

or to make things simpler:

Sum = 12 - 6 + 3 - 1.5 + 0.75 - 0.375 + 0.1875 - 0.0078125 + 0.046875 - 0.0234375

Sum = 8.078125

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