As we already have the model that describes the change of the population in Italy in terms of the years that have elapsed, we only have to replace the conditions that are requested in that equation.

Therefore to find the population of Italy in the year 2000 (t = 10 years) substitute t = 10 in the equation and have:

$p = 56.8e^{0.0015*10}\\$

$p=57.6584$ million people

To find the population of Italy in 2008 (t = 18 years)

substitute t = 18 in the equation and have:

$p=56.8e ^{0.0015*18}\\$

$p=58.3545$ million people

To predict the population in Italy for 2015 and 2020 with this model, we substitute in the equation t = 25 and t = 30

t = 25

$p=56.8e^{0.0015*25}$

$p=58.9704$ million people

t = 30

$p=56.8e^{0.0015*30}$

$p=59.4144$ million people

8 0

3 years ago

Josh is hiking glacier national park. He has now hiked a total of 17km and is 2km short of being 1/2 of the way done with his hi

Alla [95]

Answer: The total length in kilometers is 38 km

Step-by-step explanation:

17 + 2 = 19 km is 1/2 of the total length, that is,

19 = (1/2)h

(1/2)h = 19 multiply both sides by 2

h = 2*19

h = 38 km

5 0

3 years ago

Write the equation of an exponential function that passes through the points (2,48) and (5,750).

Otrada [13]

Ok, so the function form is y = a * bx.
Substitute in the values:
750 = a * b5
and
48 = a * b2
Then divide the two equations:
750/ 48 = (a * b5) / (a * b2)
So:
15.625 = b3
Take the cube root of both sides:
2.5 = b
Now, substitue b into one of the equations (the one with 48 has smaller numbers and is easier to work with.)
48 = a * 2.52
Simplify.
48 = a * 6.25
Divide both sides by 6.25
7.68 = a
Now substitute in a and b to write the exponential function:
y = 7.68 * 2.5x

7 0

3 years ago

6x2 - 5x - 4 is equivalent to:

Sophie [7]

Answer:

(2x + 1) (3x - 4)

Step-by-step explanation:

Solution:

6x² - 5x - 4
6x²- (8 - 3)x - 4
6x²- 8x + 3x - 4
2x (3x - 4) +1 (3x - 4)
(2x + 1) (3x - 4)

4 0

2 years ago