Question

A quantity with an initial value of 240 grows exponentially at a rate of 9.5% every 2 decades. What is the value of the quantity after 52 years, to the nearest hundredth?

Answer 1

Answer: 303.870087962229

Simplify ≈303.87

Explanation:

Grows 9.5%→r=0.095 Divide by 100

Grows every 2 decades: exponent of t2

(where t is in decades)

Write a function:

f(t)=240(1+0.095) ^t/2 Percent change every 2 decades

52 years→52/10→5.2 decades There are 10 years in a decade

Plug in t=5.2

f(5.2)=240(1+0.095) 5.2/2

Answer: 303.870087962229

≈303.87

Round to the nearest hundredth