Question

Given the equation y = 1.4(1.03)^x a. Does this equation represent growth or decay? b. What is the growth or decay factor? c. What is the rate of growth or decay? d. What is the initial value?

Answer 1

a. Growth

b. 1.03

c. 3%

d. 1.4

Step-by-step explanation:

In the exponential equation of the form

`y=ab^x`

The initial value is a, the growth (or decay) factor is b and the growth (or decay) rate is (b -1)*100%,

Furthermore, if b > 1 the equation represents a growth; if b < 1, then the equation represents decay.

Keeping the above in mind, we find that for the exponential function

`y=1.4(1.03)^x`

a. since 1.03 > 1, the relationship is a growth.

b. the value of b = 1.03; therefore, the growth factor is 1.03

c. The rate of growth = ( 1.03 -1 )*100% = 0.03 *100% = 3%

d. the value of a is 1.4; therefore, the initial value is 1.4.

Hence, the answers are

a. Growth

b. 1.03

c. 3%

d. 1.4