If 24n-¹ + 3 = 7 What is the value of n

In 2012, the population of a city was 5.69 million. The exponential growth rate was 2.87% per year. a) Find the exponential g

Angelina_Jolie [31]

Answer:

a) The exponential growth function

P(t) = 5,690,000(1.0287)^t

b) 6,742,868.7374 million

c) 12.04 years

d) 2439.0243902

Step-by-step explanation:

In 2012, the population of a city was 5.69 million. The exponential growth rate was 2.87% per year.

The formula for exponential growth is given as:

P(t) = Po( 1 + r) ^t

Where P = Population size after time t

Po = Initial population size

r = Growth rate in percentage

t= time in years

a) Find the exponential growth function.

P(t) = Population size after time t

Po = Initial population size = 5.69 million

r = Growth rate in percentage = 2.87% = 0.0287

t= time in years

The Exponential growth function

P(t) = 5,690,000(1 + 0.0287)^t

P(t) = 5,690,000(1.0287)^t

b) Estimate the population of the city in 2018.

From 2012 to 2018 = 6 years

t = 6 years

Hence,

P(t) = Po( 1 + r) ^t

P(t) = 5,690,000(1 + 0.0287)^6

P(t) = 5,690,000(1.0287)^6

P(t) = 6,742,868.7374 million

c) When will the population of the city be 8 million?

P(t) = 8,000,000

P(t) = Po( 1 + r) ^t

P(t) = 5,690,000(1 + 0.0287)^t

8,000,000 = 5,690,000(1 + 0.0287)^t

8,000,000 = 5,690,000(1.0287)^t

Divide both sides by 5,690,000

8,000,00/5,690,000 = 5,690,000(1.0287)^t/5,690,000

= 1.4059753954 = 1.0287^t

Take logarithm of both sides

log 1.4059753954 = log 1.0287^t

Log 1.4059753954 =t Log 1.0287

t = Log 1.4059753954/Log 1.0287

t = 12.041740264

t = 12.04 years

d) Find the doubling time.

The formula is given as 70/Growth rate

= 70/0.0287

= 2439.0243902

4 0

3 years ago

Help!!!!!!!!!!!!!!!!

Nesterboy [21]

Answer:

for Mr farley I got 70 and for Mr samuels I got also 70 and there is no difference because they both have the same mean I hope I helped

7 0

3 years ago

Find quadratic polynomial which best fits the function f(x)=e^x and x=0, in the sense that g(0)= f(0), and g'(0) = f'(0), and g"

Dmitriy789 [7]

Let $g(x)=ax^2+bx+c$ . Then

$\begin{cases}g(0)=c\\g'(0)=b\\g''(0)=2a\end{cases}$

Meanwhile, since $f(x)=e^x$ , you have $f(0)=f'(0)=f''(0)=e^0=1$ .

It follows that $a=\dfrac12$ , $b=1$ , and $c=1$ , so that the quadratic fit for $f(x)=e^x$ that satisfies the given points is

$g(x)=\dfrac12x^2+x+1$

Note that this is just the second-order Taylor polynomial for $e^x$ about $x=0$ .

3 0

4 years ago

Match each interval with its corresponding average rate of change for q(x) = (x + 3)2. 1. -6 ≤ x ≤ -4 1 2. -3 ≤ x ≤ 0 -4 3. -6 ≤

MrMuchimi

The average rate of change of a function f(x) in an interval, a < x < b is given by
$\frac{f(b) - f(a)}{b - a}$

Given q(x) = (x + 3)^2

1.) The average rate of change of q(x) in the interval -6 ≤ x ≤ -4 is given by $\frac{q(-4)-q(-6)}{-4-(-6)} = \frac{(-4+3)^2-(-6+3)^2}{-4+6} = \frac{1-9}{2} = \frac{-8}{2} =-4$

2.) The average rate of change of q(x) in the interval -3 ≤ x ≤ 0 is given by $\frac{q(0)-q(-3)}{0-(-3)} = \frac{(0+3)^2-(-3+3)^2}{0+3} = \frac{9-0}{3} = \frac{9}{3} =3$

3.) The average rate of change of q(x) in the interval -6 ≤ x ≤ -3 is given by $\frac{q(-3)-q(-6)}{-3-(-6)} = \frac{(-3+3)^2-(-6+3)^2}{-3+6} = \frac{0-9}{3} = \frac{-9}{3} =-3$

4.) The average rate of change of q(x) in the interval -3 ≤ x ≤ -2 is given by $\frac{q(-2)-q(-3)}{-2-(-3)} = \frac{(-2+3)^2-(-3+3)^2}{-2+3} = \frac{1-0}{1} = \frac{1}{1} =1$

5.) The average rate of change of q(x) in the interval -4 ≤ x ≤ -3 is given by $\frac{q(-3)-q(-4)}{-3-(-4)} = \frac{(-3+3)^2-(-4+3)^2}{-3+4} = \frac{0-1}{1} = \frac{-1}{1} =-1$

6.) The average rate of change of q(x) in the interval -6 ≤ x ≤ 0 is given by $\frac{q(0)-q(-6)}{0-(-6)} = \frac{(0+3)^2-(-6+3)^2}{0+6} = \frac{9-9}{6} = \frac{0}{6} =0$

3 0

3 years ago

Read 2 more answers

whats 12+12-12-12-12-12-12-12-12-12-21-21-21-21-21-212-12-12-21-2334-2-23-3-3-3-3-33+1802301728727498729479274732947923749237498

tino4ka555 [31]

Answer:

1.8023017e+44

Step-by-step explanation:

I hope you understand I had to convert to simplify it.

7 0

3 years ago

Read 2 more answers

If 24n-¹ + 3 = 7 What is the value of n​

If 24n-¹ + 3 = 7 What is the value of n