Question 1

Given the function $$y = 10(1.05)^t$$ representing a country's population (in millions) growing at 5% per year, what is the population after 40 years? Round your answer to the nearest million.

Accepted Answer

$$70$$ million

Question 2

A swimming pool is treated with chlorine, and the concentration $$C (in $$ppm) declines at a rate of 15% per day. If the initial concentration is $$3$$ ppm, which equation models the concentration after $$t$$ days?

Accepted Answer

$$C = 3(0.85)^t$$

Question 3

If the chlorine concentration in a pool is modeled by $$C = 3(0.85)^t$$, what will the concentration be after $$5$$ days? Round to the nearest $$0.1$$ ppm.

Accepted Answer

$$1.3$$ ppm

Question 4

Which of the following functions is exponential?

Accepted Answer

$$f(x) = 4(0.9)^x$$

Question 5

Given the function $$y = ab^x$$ and the points $$(2, 2)$$ and $$(3, 1)$$, what is the formula for the function?

Accepted Answer

$$y = 8(\frac{1}{2})^x$$

Question 6

A town's population is modeled by $$P = 25(0.95)^t. $$What is the annual percent rate of change?

Accepted Answer

$$5\%$$ decrease

Question 7

Rewrite $$y = 50(0.95)^x in $$the form $$y = ae$$^{kx}$$. What is the value of k$?

Accepted Answer

$$k = -0.0513$$

Question 8

Atmospheric pressure $$P (in $$mbar) at altitude $$A (in km) is $$modeled by $$P = 1013(0.836)^A. $$What is the pressure at the summit of Mt. Everest ($$A = 8.85 km$$)? Round to the nearest whole number.

Accepted Answer

$$347$$ mbar

Question 9

Given the function $$f(x) = 9(3)^x$$, what is the ratio of consecutive outputs when $$x$$ increases by $$1$$?

Accepted Answer

$$3$$

Question 10

Country A's population grows linearly as $$P_A = 30 + 0.5t$$ and Country B's population grows exponentially as $$P_B = 20(1.02)^t. $$After approximately how many years will Country B's population surpass Country A's?

Accepted Answer

$$51$$ years

Question 11

Which of the following best describes a function where the consecutive differences of outputs are not constant and the consecutive ratios are not constant?

Accepted Answer

Neither linear nor exponential

Question 12

If $$y = 6(0.301)^x$$, what is the value of $$y$$ when $$x = 2$$? Round to the nearest tenth.

Accepted Answer

$$0.5$$

Question 13

A town's population is modeled by $$P = 6(1.10)^t. $$What is the annual percent rate of growth?

Accepted Answer

$$10\%$$ increase

Question 14

Given $$y = ab^x$$ and $$y(7) = 35$$, $$y(3) = 48$$, what is the value of $$b$$? Round to three decimal places.

Accepted Answer

$$0.924$$

Question 15

If the atmospheric pressure at sea level is $$1013$$ mbar and at $$1.6 km $$altitude is $$835$$ mbar, what is the value of $$b in $$the exponential model $$P = ab^A$$? Round to three decimal places.

Accepted Answer

$$0.836$$

Question 16

Which town has the largest initial population given the models: $$P_1 = 10(1.05)^t$, P_2$ = 6(1.10)^t$$, $$P_3 = 25(0.95)^t$, P_4$ = 20(0.98)^t$$?

Accepted Answer

Town 3

Question 17

If $$y = 50(0.95)^x$$, what is the equivalent $$a in $$the form $$y = ae$$^{kx}$$?

Accepted Answer

$$50$$

Question 18

A population doubles every $$14.21$$ years. What is the annual percent growth rate? (Use $$P = P_0$(1 + r)^t$$ and solve for $$r.)$$

Accepted Answer

$$5\%$$

Question 19

Given $$4^x - 2^x = 16^x$$, what are the solutions for $$x$$?

Accepted Answer

$$x = 0, 2$$

Exponential and Linear Functions: Identification, Formulas, and Applications

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