What rate of interest to the nearest tenth of a percent comp

What rate of interest, to the nearest tenth of a percent, compounded annually is needed for an investment of $200 to grow to $350 in 5 years? A culture contains 1500 bacteria initially and doubles every 30 minutes. Find a function that models the number of bacteria n(t) after t minutes. Find the number of bacteria after 2 hours. After how many hours will the culture contain 4000 bacteria?

Solution

4) Amount = Principal( 1 +rate/100)^n

350 = 250(1 +r)^5

1.4 = ( 1 +r)^5

1+ r = 1.4^(1/5) = 1.0696

r = 0.0696

r = 6.96%

5) N= No(r)^n where n = minutes

2No = No(r)^30

2= r^30

r = 2^(1/30) = 2^0.033 = 1.0231

N(t) = 1500(1.0231)^n

b) n = 2hrs = 120 mi

N(120) = 1500(1.0231)^120 = 23343.72

c) N(n) = 4000

4000 = 1500(1.0231)^n

2.67 = (1.0231)^n

n = ln(2.67)/ln(1.0231) = 43 minutes