Question

A substance grows exponentially, and its weight doubles every 3 hours. Suppose it weighs 2 pounds at noon. After how many hours will it weigh 9 pounds? (Do not simplify result)

Answer 1

The substance will weigh 9 pounds after  4.5123 hours.

Here it is given that every 3 hours the weight of the substance doubles.

At 12 noon it weighed 2 pounds. Hence we will consider the initial weight to be 2.

Let the weight after x hours be w(x)

Here it doubles in 3 hours, hence the growth rate is 100%

Since the growth rate is given, the equation for the growth rate will be

w(x) = w₀.eˣ

where x = no. of 3-hour spans.

Here

w₀ = 2

and w(x) is given 9

Hence,

2eˣ = 9

or, e²ˣ = 9/2

Taking log on both sides we get

loge²ˣ = ln(9/2)

or, 2xloge = ln(9/2)

Since loge = 1 we get

2x = log(9/2)

or, x = 1.5041

Hence they will become 9 pounds after

3 X 1.5041 hours

= 4.5123 hours

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