Task Sets: Recognize constant percent rate situations - Common Core Math - HS Functions

Warm-Up: Review What You Know

Which situation describes exponential growth?

A factory produces 500 widgets per day.

A bank account earns 5% interest each year, compounded annually.

A car travels 65 miles per hour.

A candle loses 2 cm per hour as it burns.

A quantity starts at 1,000 and grows by 6% per year. What is the value after 1 year?

A function is $g(x) = 500 \cdot (1.08)^x$ . What type of function is this?

Linear — the base 1.08 acts like a slope.

Quadratic — the exponent makes it grow faster.

Exponential — it has the form $a \cdot b^x$ with constant multiplier per period.

It cannot be determined without a table.

A town grows by 3% per year. Which function models the population $P$ after $t$ years, starting from 12,000?

$P(t) = 12000 + 360t$

$P(t) = 12000 \cdot (1.03)^t$

$P(t) = 12000 \cdot (0.03)^t$

$P(t) = 12000 + 0.03t$

Which phrase signals a constant PERCENT rate situation (exponential)?

A savings account earns $150 per year.

A pool fills at 40 gallons per minute.

A medication loses 25% of its remaining amount every hour.

A store adds 50 new products each month.

A car worth $18,000 depreciates 12% per year. What is the decay factor?

Enter as a decimal (e.g., 0.88).

A culture of bacteria doubles every 4 hours. Starting with 500 cells, what is the growth factor per 4-hour period?

An exponential function has growth factor $b = 1.07$ . What is the annual percent growth rate? Enter your answer as a whole number (e.g., 7 for 7%).