Task Sets: Interpret parameters in context - Common Core Math - HS Functions

Warm-Up: Review What You Know

In the linear function $f(x) = 5x - 3$ , which value is the slope?

$-3$

$5$

$x$

$f(x)$

In the exponential function $g(x) = 750 \cdot (1.04)^x$ , what is the initial value (the value when $x = 0$ )?

In $h(x) = 2000 \cdot (0.90)^x$ , is this function growing or decaying?

Growing — the coefficient 2000 is large.

Decaying — the base $0.90 < 1$ means each period the output is multiplied by a factor less than 1.

Growing — all exponential functions grow.

Decaying — the 90 in the base is large.

A taxi fare is modeled by $C(m) = 2.80m + 12$ , where $m$ is miles driven and $C$ is cost in dollars.

(a) Interpret the slope in context (include direction, magnitude, and units).
(b) Interpret the y-intercept in context.

A cooling object's temperature is $T(t) = -3t + 90$ , where $t$ is time in minutes and $T$ is temperature in degrees Celsius.

Which interpretation of the y-intercept is correct?

The temperature decreases by 90 degrees per minute.

The initial temperature of the object is 90 degrees Celsius (at $t = 0$ ).

The temperature decreases by 3 degrees initially.

The object reaches 90 degrees after 3 minutes.

A town's population is modeled by $P(t) = 12000 \cdot (1.03)^t$ , where $t$ is years after 2015.

(a) Interpret the initial value in context.
(b) Interpret the base in context.

A car's value is modeled by $V(t) = 25000 \cdot (0.88)^t$ , where $t$ is years after purchase.

Which interpretation of the base is correct?

The car loses $0.88 in value each year.

The car loses 88% of its value each year.

Each year, the car retains 88% of its value from the previous year (loses 12% per year).

The decay factor is negative (the car is depreciating).

An exponential function has base $b = 1.065$ . What is the annual percent growth rate? Enter as a decimal (e.g., 0.065 for 6.5%).