Mathematics, 12.02.2020 05:47 pjgolden04

B) Alex invests $2000 in an account that has a 6% annual rate of growth. To the nearest year, when
will the investment be worth $3600?

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Answer from: firdausmohammed80

part 1) 10 years

part 2) 10 years

Step-by-step explanation:

The correct question is:

Part 1) Alex invests $2000 in an account that has a 6% annual rate of growth compounded annually. To the nearest year, when will the investment be worth $3600?

Part 2) Alex invests $2000 in an account that has a 6% annual rate of growth compounded continuously. To the nearest year, when will the investment be worth $3600?

Part 1) we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$P=\$2,000\\A=\$3,600\\ r=6\%=6/100=0.06\\n=1$

substitute in the formula above

$3,600=2,000(1+\frac{0.06}{1})^{t}$

$1.8=(1.06)^{t}$

Apply log both sides

$log(1.8)=log[(1.06)^{t}]$

Applying property of exponents

log(1.8)=(t)log(1.06)

t=log(1.8)/log(1.06)

$t=10.09\ years$

Round to the nearest year

$t=10\ years$

Part 2) we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$P=\$2,000\\A=\$3,600\\ r=6\%=6/100=0.06$

substitute in the formula above

$3,600=2,000(e)^{0.06t}$

$1.8=[e]^{0.06t}$

Apply ln both sides

$ln(1.8)=ln[e]^{0.06t}$

ln(1.8)=(0.06t)ln[e]

t=ln(1.8)/0.06

$t=9.80\ years$

Round to the nearest year

$t=10\ years$

Answer from: Quest

answer: idk

step-by-step explanation:

Answer from: Quest

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

Identify the transformation that maps the figure with center (7, 1) onto itself. a) rotate 180° cloc

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