Question

PLEASE HELP ME FAST!

Answer 1

Answer:

From fourth month onwards, the growth rate of $f(x)$ is greater than that of $g(x)$.

Step-by-step explanation:

Given:

The growth rates of both bank accounts are given as:

$f(x)=3^x\\g(x)=5x+25$

Now, as per question, we need to find the value of 'x' when the value of $f(x)>g(x)$. Or,

$3^x>5x+25$

Now, we can do this by checking the values of 'x' by hit and trial method.

Let $x=1$. The inequality becomes:

$3^1>5(1)+25\\3>30(False)$

Let $x=2$. The inequality becomes:

$3^2>5(2)+25\\9>35(False)$

Let $x=3$. The inequality becomes:

$3^3>5(3)+25\\27>40(False)$

Let $x=4$. The inequality becomes:

$3^4>5(4)+25\\81>45(True)$

Therefore, the value of 'x' for which $f(x)>g(x)$ is 4.

So, from the fourth month onwards, the balance in $f(x)$ becomes greater than $g(x)$.

The graphical solution is shown below to support the same.

From the graph, we can conclude that after the 'x' value equals 3.4, the graph of $f(x)$ lies above of $g(x)$. Hence, $f(x)>g(x)$ for $x>3.4$