Question

the price of silver has increased by 15% per year from 2000. in the year 2000, harry bought a silver bowl for $190. which of the following functions f(x) can be used to represent the price of the bowl x years after 2000? f(x) = 190(0.85)x f(x) = 190(1.15)x f(x) = 15(190)x f(x) = 15(0.85)x

Answer 1

Answer

f(x) = 190(1.15)x

Explanation

To solve this, we are going to use the standard exponential function:

$f(x)=a(1+b)^x$

Where

$f(x)$ is the final price after $x$ years

$a$ is the initial price

$b$ is the rate in decimal form

$x$ is the time in years

We know from our problem that the initial price is $190, so $a=190$. Now to convert the rate, 15%, to decimal form, we are going to divide it by 100%, so $r=\frac{15}{100} =0.15$. Let's replace the values:

$f(x)=a(1+b)^x$

$f(x)=190(1+0.15)^x$

$f(x)=190(1.15)^x$