find the time required for an investment of $3000 to grow to $8000 at an interest rate of 7.5% per year, compounded quarterly ( round the answer to two decimal places)​

8000 = 3000(1 + 0.065/4)4n

8000/3000 = (1 + 0.065/4)4n

ln(8000/3000) = 4nln(1 + 0.065/4)

n = ln(8000/3000)/4ln(1 + 0.065/4)

n = 15.21

6e14 is the answer.

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true