Round this number the nearest hundredth 7.349

The function f(x) = 4(4)x represents the growth of a fly population every year in a remote swamp. Jackie wants to manipulate the

Sauron [17]

The function f(x) = 4(4)x represents the growth of a fly population every year in a remote swamp.

calculates three times a year, not just once a year.

$f(x)= 4(4)^x$

3 times a year

so x becomes 3x

$f(x)= 4(1+r)^{3x}$

$4(4)^x=4(1+r)^{3x}$

Take log on both sides

$log(4)^x=log(1+r)^{3x}$

Use log property and move exponent before log

$xlog(4)=3xlog(1+r)}$

Divide both sides by x

log 4 = 3 log(1+r)

Solve for '1+r'

log 4 = log(1+r)^3

Remove log from both sides

4 = (1+r)^3

take cube root on both sides

1.584740= 1+r

1+r = 1.59

$f(x)= 4(1+r)^{3x}$

so equation becomes

$f(x)= 4(1.59)^{3x}$

1+r = 1.59

subtract 1 from both sides

So r= 59 = 59%

So growth factor is 59%

Answer is option C

5 0

3 years ago

Find the perimeter of the triangle defined by the coordinates (7, 1), (-6, 1), and (10, 6). (Round to nearest tenth)

matrenka [14]

Answer:

$35.6\ units$

Step-by-step explanation:

we know that

The perimeter of triangle is equal to the sum of the length of the three sides

Let

$A(7, 1), B(-6, 1), C(10, 6)$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the distance AB

$A(7, 1), B(-6, 1)$

substitute in the formula

$d=\sqrt{(1-1)^{2}+(-6-7)^{2}}$

$d=\sqrt{(0)^{2}+(-13)^{2}}$

$dAB=13\ units$

Find the distance BC

$B(-6, 1), C(10, 6)$

substitute in the formula

$d=\sqrt{(6-1)^{2}+(10+6)^{2}}$

$d=\sqrt{(5)^{2}+(16)^{2}}$

$dBC=16.8\ units$

Find the distance AC

$A(7, 1), C(10, 6)$

substitute in the formula

$d=\sqrt{(6-1)^{2}+(10-7)^{2}}$

$d=\sqrt{(5)^{2}+(3)^{2}}$

$dAC=5.8\ units$

Find the perimeter

$P=dAB+dBC+dAC$

$P=13+16.8+5.8=35.6\ units$

4 0

3 years ago

Graph a direct variation function that goes through the point (-2, -6). what is the slope

Effectus [21]

Answer:

The slope is 3.

Step-by-step explanation:

A direct variation function will always go through the origin point (0, 0).

Therefore, we have the two points (0, 0) and (-2, -6).

We can use the slope formula to find the slope:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Substitute and evaluate:

$\displaystyle m=\frac{0-(-6)}{0-(-2)}=\frac{6}{2}=3$

Therefore, the slope of the function is 3.

To graph, simply plot (0, 0) and (-2, -6) and draw a line connecting them. This is shown below.

6 0

2 years ago

Read 2 more answers

If theperimeter of the triangle ABC is 23, find the length of each side.

aalyn [17]

You can't.
There isn't enough evidence/proof to prove the length of each side.<span />

6 0

3 years ago

4|w − 5| = 4

anastassius [24]

Answer:

w = 9 or w = 1

Step-by-step explanation:

4|w − 5| = 4

Divide both sides by 4

w - 5 = 4 w - 5 = -4

+ 5 + 5 + 5 + 5

w = 9 w = 1

7 0

3 years ago