Algebra Answers

Alex can read 5 pages in 3 minutes. Based on this rate, what is the total amount of pages Alex will read if he spends 27 minutes reading? 

A town has a population of 14000 and grows at 2.5% every year. What will be the population after 5 years, to the nearest whole number?

The value of a car after it is purchased depreciates according to the

A formula V(n) 5 25 000(0.85)n, where V(n) is the car’s value in the

nth year after it was purchased.

a) What is the purchase price of the car?

b) What is the annual rate of depreciation?

c) What is the car’s value at the end of 3 years?

d) How much value does the car lose in its first year?

e) How much value does it lose in its fifth year?

f) After how many years will the value of the car be half of the

original purchase price?

Gels used to change the colour of spotlights each reduce the intensity of the light by 4%. The algebraic model for this situation is

I 5 100(0.96)n.

a) Describe what each part of the equation represents.

b) Determine the intensity of the spotlight if three gels are used.

c) How many gels would reduce the intensity by more than 75%?

*CREATE a real-life exponential growth OR exponential decay word problem using real numbers and formulas

*determine where we see exponential growth and exponential decay in real life. For example, an exponential growth function can model the number of COVID-19 cases with respect to time. Reminder: DO NOT solve your problem. You simply need to create the question. 

An ant colony triples in number every month. Currently, there are 24 000 in the nest.

a) What is the monthly growth rate of the colony? What is the initial population?

b) Write an equation that models the number of ants in the colony, given the number of months.

c) Use your equation to predict the size of the colony in three months.

d) Use your equation to predict the size of the colony five months ago.

Five hundred yeast cells in a bowl of warm water doubled in number

A every 40 min.

a) Create a graph of the number of yeast cells versus time.

b) Use the graph to determine how long it would take for the total

number of cells to triple (to the nearest minute).

c) Describe how you can adapt your graph to determine the number

of cells for the time before they were monitored.

In each case, write an equation that models the situation described.

a) An antique is purchased for $5000 in 1990. It appreciates in value

by 3.25% each year.

b) A town had 2500 residents in 1990. It grew at a rate of 0.5% per

year for t years.

c) A single bacterium of a particular type takes one day to double.

The population is P after t days.

The number of guppies in an aquarium is modelled by the function

K N(t) 5 12(1 1 0.04)t, where t is measured in weeks.

a) Describe what each part of the equation represents.

b) Determine the number of guppies in the aquarium after 10 weeks.

c) Will this equation always model the population in the aquarium?

The size of a yeast culture is measured each hour, and the results are displayed on the graph shown.

a) From the graph, estimate the initial number of yeast cells.

b) Estimate the number of cells after 30 h.

c) Use the initial amount to estimate the length of time required for the number of cells to double.

d) Use an amount (other than the initial amount) to determine the length of time required for the number of cells present at that time to double.

e) Describe what you noticed about the two doubling times. Check what you found with a different amount from the graph.