A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:
Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8
Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2 Therefore:
To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x
Exponential change can be modeled by: N = N(0) x λⁿ; where λ is the rate of change. It is greater than 1 when there is growth and less than 1 when there is decay. n is the number of time periods passed. λ is 1 + 0.083 = 1.083 N(0) is the initial value of 750 n is 2050 - 2005 = 45 years N = 750 x (1.083)⁴⁵ = 27,000 fish
