paolo invests his money in a savings account. the function $f(x)=600(1.02)^x$ models the balance in his…
paolo invests his money in a savings account. the function $f(x)=600(1.02)^x$ models the balance in his account after $x$ years. by what percentage is the balance changing each year?\n1.02%\n2%\n6%\n20%
Answer
Explanation:
Step1: Identify the compound - growth formula form
The general form of an exponential - growth function is $y = a(1 + r)^x$, where $a$ is the initial amount, $r$ is the rate of growth as a decimal, and $x$ is the number of time periods. In the given function $f(x)=600(1.02)^x$, we can compare it with the general form.
Step2: Determine the growth rate
We have $1 + r=1.02$. Solving for $r$, we subtract 1 from both sides: $r = 1.02−1=0.02$.
Step3: Convert the decimal to a percentage
To convert the decimal $r = 0.02$ to a percentage, we multiply by 100. So, $0.02\times100 = 2%$.
Answer:
2%