Problema Solution
When their child was born, her parents invested $40,000 in a plan guaranteed to increase by 3% per year. The logarithmic function y equals 77.9 log start fraction x over 40,000 end fraction can be used to determine the number of years, y, it takes for the investment to be worth x dollarsAfter how many years will the investment be worth approximately 50% more than it was originally and how old will their child be when the investment is worth about $100,000?
Answer provided by our tutors
y = 77.9 log(x/40,000)
We need to find y when x = 40,000 + 0.50*40,000:
Plug x = 60,000 into y = 77.9 log(x/40,000)
y = 77.9 log(60000/40000)
y = 14 years approximately
After 14 years the investment will be worth approximately 50% more than it was originally.
Next we need to find y when x = $100,000:
y = 77.9 log(100000/40000)
y = 31 years approximately
The child will be 31 years old when the investment is worth $100,000.