Suppose that $18,000 is invested in a bond fund and the account grows to $23,344.74 in 5 yr. a. use the model a = pert to determine the average rate of return under continuous compounding. round to the nearest tenth of a percent. b. how long will it take the investment to reach $30,000 if the rate of return continues? round to the nearest tenth of a year

a. 5.2%

b. 9.8 years

Step-by-step explanation:

a. Put the given numbers in the formula and solve for r.

... 23,344.74 = 18,000×e^(r·5)

... 23,344.74/18,000 = e^(5r) . . . . . divide by 18000

... ln(1.29693) = 5r . . . . . . . . . . . . . . take the natural logarithm

... 0.26/5 = r = 0.052 = 5.2% . . . . . divide by 5

The rate of return is 5.2%, compounded continuously.

b. Put the given numbers in the formula and solve for t.

... 30,000 = 18,000×e^(0.052t)

... 30,000/18,000 = e^(0.052t) . . . . . divide by 18,000

... ln(5/3) = 0.052t . . . . . . take the natural log

... 0.510826/0.052 = t = 9.8 . . . . . divide by the coefficient of t

It will take 9.8 years for the investment to reach $30,000.

line or a linear equation graph

step-by-step explanation:

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.