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 and growth factor

The initial amount $a$ is the current earnings. Dan's business earned $85000$ this year, so $a = 85000$. The growth rate is $12%=0.12$. The growth factor $b$ for an exponential - growth model $y=a(b)^x$ is $b = 1 + r$, where $r$ is the growth rate. So $b=1 + 0.12=1.12$.

Step2: Write the exponential equation

The exponential equation is $y = 85000(1.12)^x$.

Step3: Calculate the earnings in 5 years

Substitute $x = 5$ into the equation $y = 85000(1.12)^x$. We have $y=85000\times(1.12)^5$. First, calculate $(1.12)^5=1.12\times1.12\times1.12\times1.12\times1.12\approx1.76234$. Then $y = 85000\times1.76234=149798.9$. Rounding to the nearest hundred dollars, $y\approx150000$.

Answer:

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