Answer :
it take 16 years for your salary to reach $75,000 .
Step-by-step explanation:
Here we have , Your starting salary at a new company is $45,300 and it increase by 3.25% each year. How many years will it take for your salary to reach $75,000. Let's find out:
Let t be the number of years after which $45,300 is increased to $75,000 at increase of 3.25% . So , equation from the above statement is given as :
⇒ [tex]75000 = 45300( 1 + \frac{3.25}{100} )^t[/tex]
⇒ [tex]75000 = 45300( 1 +0.0325 )^t[/tex]
⇒ [tex]75000 = 45300( 1.0325 )^t[/tex]
⇒ [tex]\frac{75000}{45300} = ( 1.0325 )^t[/tex]
⇒ [tex]( 1.0325 )^t = 1.65562914[/tex]
Taking anti log with base 1.0325:
⇒ [tex]t = Log_1._0_3_2_5(1.65562914)[/tex]
⇒ [tex]t = 15.76[/tex]
On rounding off we get :
⇒ [tex]t = 16[/tex]
Therefore , it take 16 years for your salary to reach $75,000 .