given the exponential equation ( y = 4738(1.06)^t ), identify the following:\na) initial value:\nb) rate of…

given the exponential equation ( y = 4738(1.06)^t ), identify the following:\na) initial value:\nb) rate of change:\nc) growth or decay:

given the exponential equation ( y = 4738(1.06)^t ), identify the following:\na) initial value:\nb) rate of change:\nc) growth or decay:

Answer

Explanation:

Step1: Identify the initial value

The general form of an exponential function is (y = a(1 + r)^t), where (a) is the initial value. In the given function (y = 4738(1.06)^t), when (t = 0), (y=4738(1.06)^0=4738\times1 = 4738).

Step2: Identify the rate of change

Compare (y = 4738(1.06)^t) with (y=a(1 + r)^t). We have (1 + r=1.06), so (r=1.06 - 1=0.06 = 6%)

Step3: Determine growth or decay

Since (r = 0.06>0) (or (1 + r=1.06>1)), the function represents growth.

Answer:

a) (4738) b) (6%) c) Growth