dans small business earned about $85,000 this year. based on data from similar businesses, dan expects his…

dans small business earned about $85,000 this year. based on data from similar businesses, dan expects his annual earnings to increase by 12% each year. write an exponential equation in the form y = a(b)^x that can model dans annual earnings, y, in x years. use whole numbers, decimals, or simplified fractions for the values of a and b. y = to the nearest hundred dollars, how much is dans small business predicted to earn in 5 years? $

dans small business earned about $85,000 this year. based on data from similar businesses, dan expects his annual earnings to increase by 12% each year. write an exponential equation in the form y = a(b)^x that can model dans annual earnings, y, in x years. use whole numbers, decimals, or simplified fractions for the values of a and b. y = to the nearest hundred dollars, how much is dans small business predicted to earn in 5 years? $

Answer

Explanation:

Step1: Identify the initial value a

The initial earnings this year is $85000$, so $a = 85000$.

Step2: Identify the growth - factor b

The earnings increase by 12% each year. The growth - factor $b=1 + 0.12=1.12$.

Step3: Write the exponential equation

The exponential equation is $y = a(b)^x$, substituting $a = 85000$ and $b = 1.12$ we get $y=85000(1.12)^x$.

Step4: Calculate the earnings in 5 years

Substitute $x = 5$ into the equation $y=85000(1.12)^5$. First, calculate $(1.12)^5=1.12\times1.12\times1.12\times1.12\times1.12\approx1.76234$. Then $y = 85000\times1.76234=149898.9$. Rounding to the nearest hundred dollars, $y\approx150000$.

Answer:

$y = 85000(1.12)^x$ $150000$