Algebra 2 · Unit 5 · Mid-Unit Assessment
Algebra 2 · Unit 5 · Mid-Unit Assessment
Exponential Growth, Decay, & Half-Life
Name
Period
Date
Show your work in the dashed box for each problem. Calculators allowed. Extra credit in violet on the back of the page — a sentence using math vocabulary, no word bank.
General form:   \(F(t) = a \cdot b^{\,t}\)  —  where a is the starting value, b is the growth or decay factor, and t is the time at evaluation.

1. Algae in the Pond  (growth — doubling)

An algae bloom is first observed covering 25% of a pond's surface. The area covered doubles every day.

(a) Using the General form listed at the top of the first page, write a function \(A(t)\) for the percent of the pond covered, where \(t\) is days since first observation.
(b) What percent of the pond is covered after 1 day?
(c) How many days until the pond is fully covered (100%)?
Space for work
(a) \(A(t) = \)   (b) %   (c) days

2. Radioactive Dating  (find the age from remaining isotope)

A piece of charcoal from an ancient campfire has 0.5 picograms of carbon-14 today. When it was burned, it would have contained about 4 picograms. Carbon-14 has a half-life of 5,730 years.

(a) How many half-lives have passed since the wood was burned?
(b) How old is the charcoal, in years?
(c) Using the General form listed at the top of the first page, write a function \(C(t)\) for the picograms of carbon-14 remaining, where \(t\) is years since the wood was burned.
Space for work
(a) half-lives   (b) years   (c) \(C(t) = \)
Page 1 of 2 · Algebra 2 · Unit 5 · Mid-Unit Assessment
Algebra 2 · Unit 5 · Mid-Unit Assessment
Exponential Growth, Decay, & Half-Life
Name
Period

3. Union vs Non-Union Pay  (comparison)

Two workers start at $40,000 per year. The union worker's pay grows by a factor of 1.04 each year (negotiated cost-of-living raise). The non-union worker's pay grows by a factor of 1.015 each year.

(a) Using the General form listed at the top of the first page, write both pay functions in thousands of dollars, where \(t\) is years worked.
(b) After 10 years, how much does the union worker make? The non-union worker?
(c) What is the dollar gap between them at year 10?
Space for work
(a) \(U(t) = \) , \(N(t) = \)   (b) \(U(10) \approx \$\)K, \(N(10) \approx \$\)K   (c) gap \(\approx \$\)K
Extra credit Use math vocabulary to complete: "In the union worker's pay function, the number $40,000 represents the — the salary when \(t = 0\). The number 1.04 represents the per-year ."
Page 2 of 2 · Algebra 2 · Unit 5 · Mid-Unit Assessment