Olivia invested $2,400 in an account paying an interest rate of 4.6\% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $3,550 ?

  8.5

Step-by-step explanation:

For continuous compounding, the account value formula is ...

  A = Pe^(rt)

where P is the invested amount, r is the annual interest rate, and t is the number of years. We want to find t when ...

  3550 = 2400e^(.046t)

  ln(355/240) = 0.046t

  t = ln(355/240)/0.046 ≈ 8.5

It will take 8.5 years for the value to reach $3550.

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1