Question

Identify the percent increase or decrease for exponential growth if:
y = 5^x

Answer 1

Answer: 500%

Step-by-step explanation:

It is growing because the base is greater than 1 and the exponent has a positive sign

Answer 2

Hence, it is exponential growth.

To understand the calculations, check below.

Exponential Function:

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations, and so on.

Exponential functions are in the form $y=ab^{x}$

• If a is +ve and $b > 1$ the exponential growth.
• If b is less than $1$ but $b > 0$ then exponential decrease.

Here $y=5^{x}$.

Here, $a=1 \ and \ b=5 > 1$

Hence it is exponential growth

Again exponential can be represented by,

$y=a(1+r)^{x}$ where $(1+r) is \ replaced \ by 'b'.$

Here

$1+r=b\\\therefore b=5\\1+r=5\\r=5-1\\r=4$

Growth rate in percentage=$400$%.

Verification:

$y=5^{x} , \ put \ x=1$

$y=5,$

$y=5^{x} \ put \ x=2$

$y=5^{2} =25$

Growth$=25-5=20$

In percentage$=\frac{growth}{initial \ value} \times100$

Percentage$=\frac{20}{5} \times100$

                  $=400$%.

Learn more about the topic of Exponential Function: https://brainly.com/question/25942338