Question

The following function represents exponential growth or decay.

P= 2.9(1.05)^t

a. The initial quantity is :_______________
b. The initial quantity is :__________
c. Is the quantity growing or decaying?

Answer 1

a) The initial quantity is 2.9.

b) The initial quantity is 2.9.

c) The multiplier is 1.05 > 1, and thus, the quantity is growing.

Explanation:

Exponential equations:

Have the following format:

`A(t) = A(0)(k)^t`

In which A(0) is the initial amount and k is the multiplier.

If k > 0, the quantity is growing.

If k < 0, the quintity is decaying.

In this question:

`P(t) = 2.9(1.05)^t`

a, b. The initial quantity is

P(0). So

`P(0) = 2.9(1.05)^0 = 2.9*1 = 2.9`

The initial quantity is 2.9.

c. Is the quantity growing or decaying?

The multiplier is 1.05 > 1, and thus, the quantity is growing.