Preview of Inverse, Exponential, and Logarithmic Functions
Terms for Topic "Inverse, Exponential, and Logarithmic Functions"
Summary and Analysis
- Inverse Functions
- Problems for "Inverse Functions"
- The Number e and the Natural Log
- Problems for "The Number e and the Natural Log"
- Derivatives of ex and of the Natural Log
- Problems for "Derivatives of ex and of the Natural Log"
- Exponential Growth and Decay
- Problems for "Exponential Growth and Decay"
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Inverse, Exponential, and Logarithmic Functions

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Problems for "Exponential Growth and Decay"

Problem : If P = 300e ^2t , at what time will P=600?

Problem : A strain of bacteria multiply in such a fashion that they double in number every 4 hours. Find an expression that describes this kind of growth.

Solution for Problem 2 >>

A function that grows or decays by a fixed percentage over time exhibits growth of the form

B(t) = B ₀ e ^kt

After 4 hours, B(t) = 2B ₀ , so 2B ₀ = B ₀ e ^k(4) , 2 = e ^4k Use natural log to solve for k

ln(2)		= 4k
k		= .173
B(t)		= B ₀ e ^.173t

Problem : Find a function that meets the following:

= 0.693y

Solution for Problem 3 >>

Problem : The half-life of a substance is the time that it takes for the mass of that substance to decay to 50% of its original value. If a certain substance has a half-life of 30 minutes, what is an equation that describes its decay?

Solution for Problem 4 >>

This is another case of exponential decay, because a certain percentage of the substance decays at regular time intervals. So, the general form is

C(t) = C ₀ e ^kt

At t = 30 , 1/2 of the original remains, so