31. The incidence of a disease (Continuation of Example 4.) Suppose that in any given year the number of cases can be reduced by 25% instead of 20%.
b. How long will it take to eradicate the disease—that is, reduce the number of cases to less than 1?

23. Human evolution continues The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years.

c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?

31. The incidence of a disease (Continuation of Example 4.) Suppose that in any given year the number of cases can be reduced by 25% instead of 20%.

a. How long will it take to reduce the number of cases to 1000?

37. Plutonium-239 The half-life of the plutonium isotope is 24,360 years. If 10 g of plutonium is released into the atmosphere by a nuclear accident, how many years will it take for 80% of the isotope to decay?

23. Human evolution continues The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years.

a. If t represents time in years and y represents tooth size, use the condition that y=0.99y_0 when t=1000 to find the value of k in the equation y=y_0 e^(kt). Then use this value of k to answer the following questions.

Determine if the function is an exponential function.  

If so, identify the power & base, then evaluate for $x=4$.

$f\(\left\)(x\(\right\))=\(\left\)(-2\(\right\))^{x}$

Determine if the function is an exponential function.  

If so, identify the power & base, then evaluate for $x=4$ .

$f\(\left\)(x\(\right\))=3\(\left\)(1.5\(\right\))^{x}$

Determine if the function is an exponential function.  

If so, identify the power & base, then evaluate for $x=4$ .

$f\(\left\)(x\(\right\))=\(\left\)(\(\frac\)12\(\right\))^{x}$

Graph the given function.

$g\(\left\)(x\(\right\))=e^{x+3}-1$