19. Starting at the age of 40 , an average man loses \( 5 \% \) of his hair every year. At what age should an average man expect to have half his hair left?

By the time an average man reaches 40 years old, he starts losing 5% of his hair annually. To find out when he can expect to have half of his hair left, we can utilize the formula for exponential decay. Specifically, we look at the function \( H(t) = H_0 \times (0.95)^t \), where \( H_0 \) is the initial amount of hair, \( t \) is the time in years, and 0.95 represents the remaining hair after each year. Solving for \( t \) when \( H(t) = 0.5 H_0 \) gives us the equation \( 0.5 = (0.95)^t \). Taking the logarithm of both sides and rearranging provides a solution for \( t \) of about 14.2 years. Thus, an average man can expect to be around 54 years old when he has half of his hair left. Hair loss might feel like an inevitable rite of passage, but it’s essential to remember that genetics play a significant role! Many men notice noticeable hair thinning or balding patterns earlier, while others may retain a full head of hair well into their later years. There are treatments and styles to embrace this change positively, so don’t let hair loss bring you down—a confident attitude is a key style that never fades!