The long jump record, in feet, at a particular school can be modeled by f(x)=20.4+2.1ln(x+1) where x is the number of years since records began to be kept at the school. What is the record for the long jump 8 years after record started being kept? Round your answer to the nearest tenth and do not enter the units.
To find the record for the long jump 8 years after the records started being kept, we need to substitute x = 8 into the equation f(x) = 20.4 + 2.1ln(x+1).
f(8) = 20.4 + 2.1ln(8+1)
= 20.4 + 2.1ln(9)
≈ 20.4 + 2.1(2.197)
≈ 20.4 + 4.6137
≈ 24.0
Rounded to the nearest tenth, the record for the long jump 8 years after records started being kept is 24.0.
To find the record for the long jump 8 years after records started being kept at the school, we need to substitute x = 8 into the equation f(x) = 20.4 + 2.1ln(x + 1).
Let's calculate it step by step:
1. Substitute x = 8 into the equation:
f(8) = 20.4 + 2.1ln(8 + 1)
2. Simplify the expression:
f(8) = 20.4 + 2.1ln(9)
3. Evaluate the natural logarithm of 9:
ln(9) ≈ 2.197
4. Substitute this value back into the equation:
f(8) = 20.4 + 2.1(2.197)
f(8) ≈ 20.4 + 4.612
f(8) ≈ 24.012
Therefore, the record for the long jump 8 years after records started being kept at the school is approximately 24.0 feet.