Question

Find the initial value aa, growth/decay factor bb, and growth/decay rate rr for the following exponential function: Q(t)=0.0019(2.22)−3t Q(t)=0.0019(2.22)−3t (a) The initial value is a=a= help (numbers) (b) The growth factor is b=b= help (numbers) (Retain at least four decimal places.) (c) The growth rate is r=r= % help (numbers) (Ensure your answer is accurate to at least the nearest 0.01%) (Note that if rr gives a decay rate you should have r<0r<0.)

Answer 1

Answer:

a) 0.0019

b) 0.0913

c) 9.13%

Step-by-step explanation:

We are given the following information in the question:

$Q(t)=0.0019(2.22)^{-3t}$

The standard form of exponential function is

$f(t) = ab^{t}$

where a is the initial amount and b is the base.

Rewriting the the given function, we have:

$Q(t)=0.0019(2.22)^{-3t}\\Q(t)=0.0019((2.22)^{-3})^t\\Q(t)=0.0019(0.0913)^t$

a) Initial Value

Putting t = 0, we get,

$Q(0)=0.0019(0.0913)^0 = 0.0019$

a = 0.0019

b) Growth factor

Comparing, we get, b = 0.0913

c) Growth rate

$\text{Growth factor}\times 100\% = 0.0913\times 100\% = 9.13\%$