MATHEMATICS MIDDLE SCHOOL

PLEASE HELP ME FAST!The balance in two separate bank accounts grow each month at different rates. The growth rates for both accounts are represented by the functions f(x)=3^x and g(x)=5x+25. In what month is the f(x) balance greater than the g(x) balance? Show your work!
P.S Whoever gives me a good answer and shows their work I will make as Brainliest!

Answers

Answer 1

Answer:

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:

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

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:

$3^1>5(1)+25\n3>30(False)$

Let $x=2$ . The inequality becomes:

$3^2>5(2)+25\n9>35(False)$

Let $x=3$ . The inequality becomes:

$3^3>5(3)+25\n27>40(False)$

Let $x=4$ . The inequality becomes:

$3^4>5(4)+25\n81>45(True)$

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 $x>3.4$

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Expert verified FOX DUNG!

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