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# Math quiz 4-5

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

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