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.
4. Moon Base Population (growth — per decade)
In a video game, Jada is building a moon base to support a growing population. Her base has a population of 32,000 in the year 2200. The population grows exponentially by about 50% per decade.
(a) What is the starting value \(a\)? \(a = \)
(b) What is the growth factor \(b\)? \(b = \)
(c) Using the General form listed at the top of the first page, write a function \(P(d)\) for the population, where \(d\) is the number of decades after 2200.
\(P(d) = \)
(d) Predict the population in 2210 (one decade after 2200). people
(e) Predict the population in 2218 (18 years is ?? decades after 2200). \(\approx\) people
Space for work
5. Rare Pokémon Card (growth — read a table)
The table shows the resale value of a rare 1st edition Pokémon card over time.
Years \(t\)
0
1
2
3
4
Value (\$)
16
24
36
?
?
(a) What is the per-year growth factor \(b\)? \(b = \)
(b) Fill in the missing values for \(t = 3\) and \(t = 4\). \(V(3) = \$\) \(V(4) = \$\)
(c) What is the starting value \(a\)? \(a = \$\)
(d) Using the General form listed at the top of the first page, write a function \(V(t)\) for the card's value in dollars.
\(V(t) = \)
(e) Predict the card's value at \(t = 5\). \(V(5) = \$\)
Space for work
Page 1 of 2 · Algebra 2 · Unit 5 · Mid-Unit Assessment · Part 2
Algebra 2 · Unit 5 · Mid-Unit Assessment · Part 2
Exponential Growth, Decay, & Graphs
Name
Period
6. Reading a Graph (identify parameters from the graph)
The graph below shows a function \(f(t)\) modeling the amount of a substance remaining over time, in years.
(a) What is the y-intercept (starting value \(a\))?
\(a = \)
(b) Looking at \(t = 0\) and \(t = 1\), the value goes from 320 to 160. What is the decay factor \(b\)?
\(b = \)
(c) Using the General form listed at the top of the first page, write \(f(t)\).
\(f(t) = \)
(d) Use your function to predict \(f(5)\).
\(f(5) \approx \)
Space for work
Extra credit
Use math vocabulary to complete: "The function shown is exponential (circle one) growth / decay because \(b\) is greater than 0 and less than . The is 320, and as \(t\) increases the value (circle one) increases / decreases."
Page 2 of 2 · Algebra 2 · Unit 5 · Mid-Unit Assessment · Part 2