Answer:
6 years
Step-by-step explanation:
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:
[tex]y=ab^x[/tex]
Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8
[tex]y=ab^x\\8=ab^0\\a=8[/tex]
Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2
Therefore:
[tex]y=ab^x\\y=8(1.2^x) \\[/tex]
To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x
[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]
x = 6 years to the nearest year
