Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

Normal Size Small Size show me how

Normal Size Small Size show me how

# Math quiz 4-5

### Math of Motion College course Quiz chapters 4-5

Question | Answer |
---|---|

Exponential functions are functions that increase or decrease at a constant rate. | True. If the constant rate is r then the formula is f(t)=a*(1+r)^t. The function decreases when 0<1+r<1 and increases when 1+r>1. |

If y=40(1.05)^t then y is an exponential function of t. | True. |

If your salary,s, grows by 4% each year then S=s0(004)^t where t is in years. | False. The annual growth factor would be 1.04 so s=s0(1.040)^t. |

If f(t)=3(2/5)^t then t is a decreasing function | True. Because 2/5 equals .4 which is less than 1 which means it is decreasing. |

If Q=f(t)=ab^t then a is the initial value of Q | True. The initial value of Q when t=0, so Q=f(0)=a*b^0=a*1=a |

A population that has 1000 members and is decreasing 10% per year can be modeled as P=1000(0.10)^t. | False. Because it is decreasing it is (1-r) if r=.10 then it would be P=1000(.9)^t |

A possible formula for an exponential function that passes through the point (0,1) and the point (2,10) is y=4.5t+1. | False. This is the formula of a linear function. |

In the formula Q=ab^t, the value of a tells us where the graph crosses the Q-axis | True. |

Exponential graphs are always concave up. | False. It is only concave up when a>0 and b>1 or a>0 and 0 |

If a population has 200 members at time 0 and was growing at 4% per year, then the population size after t years can be expressed as p=200(1.04)^t | True. The initial value is 200 and the growth factor is 1.04 |

If P=4e^-0.90t, we say the continuous growth rate of f=10% | False |

If Q=Q0e^kt, with Q0 positive and k negative, then Q is decreasing. | True. Since K is the continuous growth rate and negative, Q is decreasing. |

If a $500 investment earns 6% per year, compounded quarterly, we can find the balance after 3 years by evaluating the formula: B=500(1+6/4)^3*4 | False. B=500(1 + .06/4)^3*4. |

Investing $10,000 for 20 years at 5% earns more if interest is compounded quarterly than if it's compounded annually. | True. The interest from any quarter is compounded in subsequent quarters. |

There is no limit to the amount a 20 year $10,000 investment at 5% interest can earn if the number of times the interest is compounded becomes greater and greater. | False |

The log of 2000 is less than 3 | False. Since the log 1000_log10^3=3 we know log2000>3 or use calculator to find log2000 is about 3.3. |

If 2^x=1024 then x=10 | True. Calculate 2^1024 and you get 10. |

If the function y=ab^t is converted to y=ae^kt, K is always equal to lnB | True. Comparing the equation we see b=e^k, so k=lnB |

If 10^y=X then logx=y | True. |

For any N we have log(10^n)=n | True. The log function outputs the power of 10 which in this case is n |

If a and b are positive, log(a/b)=loga/logb | False. Because according to the qquotient rule it would be loga-logb |

For any value a, loga=lna | False. For example log10=1, but ln10=2.3026 |

The function y=logx has an asymptote at y=o | False. It would have an asymptote at x=0 |

The reflected graph of y=logx across the line y=x is the graph of y=10^X | True because the two functions are inverses of one another. |

The function y=log(b^t) is always equal to y=(logb)^t | False.Because it's the log of the whole value of b^t not just b. |

If 7.32=e&t then t=7.32/e | False. Taking the natural log of both sides we see t=ln7.32 |

If ab^t=n then t=log(n/a)/logb | True. |

The half-life of a quantity is the time it takes for the quantity to be reduced by half. | True. By definition |

If y=6(3)^t, then y=6e^(ln3)t | True. |

If Q=Qoe^kt, then t=ln(Q/Q0)/k | True. Solve for t by dividing both sides by Qo taking ln of both sides then dividing by k. |

One million and one billion differ by one order of magnitude. | False. |

Given the points on a cubic curve (1,1), (2,8) , (3,27) and (4,64) it is not possible to fit an exponential function to this data. | False. The fit will not be as good as y=x^3 but an exponential function can be found. |

Created by:
turtlefan1818