Question

Given the equation y = 10(1.05), determine whether it represents growth or decay and calculate the percentage of increase or decrease.

a) The equation represents growth, with a 5% increase.
b) The equation represents decay, with a 5% decrease.
c) The equation represents growth, with a 105% increase.
d) The equation represents decay, with a 105% decrease.

Answer 1

The equation y = 10(1.05) represents exponential growth with a 5% increase each time the variable x increases by one unit.

Step-by-step explanation:

The equation provided, y = 10(1.05), indicates that for every unit increase in x, y is multiplied by 1.05. This factor of 1.05 represents a 5% increase each time x increases by one unit. Hence, the equation signifies exponential growth, not decay. To determine the percentage increase, we need to compare the growth factor to the value 1, which represents no change. Since 1.05 is greater than 1, it means that the value of y is increasing by 5% over the original amount. Therefore, the correct choice is (a) The equation represents growth, with a 5% increase.