Question

The values of y = 10' increase rapidly as large values of x become larger. Calculate the value of y when x = 5 and x = 5.1. What is the increase in y for this small change in x?

A) 27,050.30
B) 25,892.54
C) 26,116.42
D) 25,800.12

Answer 1

The increase in y for this small change in x is 25,800.12.

None of the given options is answer.

Step-by-step explanation:

Given the exponential relationship between x and y, where y = 10^x, as x increases, the values of y increase rapidly. When x = 5, y = 10^5 = 100,000. When x = 5.1, y = 10^5.1 = 127,483.09. Therefore, the increase in y for this small change in x is 127,483.09 - 100,000 = 27,483.09.

Steps to solve:

Calculate the value of y when x = 5:

y = 10^5 = 100,000

Calculate the value of y when x = 5.1:

y = 10^5.1 = 127,483.09

Calculate the increase in y:

increase_in_y = y2 - y1

increase_in_y = 127,483.09 - 100,000 = 27,483.09

Answer:

The increase in y for this small change in x is 27,483.09.

None of the given options is answer.