In $1970,$ the CPI was $37.8,$ and in $2000,$ the CPI was $168.8 .$ This means that an urban consumer who paid 37.80 dollars for a market basket of consumer goods and services in 1970 would have needed 168.80 dollars for similar goods and services in $2000 .$ Find a simple exponential function of the form $y=a b^{\prime}$ that models the CPI for $1970-2000,$ and predict its value for 2020. (a) Find the amount of light at a depth of 2 meters. A drug is eliminated from the body through urine. (a) Find the monthly payment on a 30 -year 250,000 dollars home mortgage if the interest rate is $8 \%$(b) Find the total interest paid on the loan in part (a). The declining balance method is an accounting method in which the amount of depreciation taken each year is a fixed percentage of the present value of the item. Some lending institutions calculate the monthly payment $M$ on a loan of $L$ dollars at an interest rate $r$ (expressed as a decimal) by using the formula $$M=\frac{L r k}{12(k-1)}$$ where $k=[1+(r / 12)]^{12 t}$ and $t$ is the number of years that the loan is in effect.Business loan The owner of a small business decides to finance a new computer by borrowing 3000 dollars for 2 years at an interest rate of $7.5 \%$(a) Find the monthly payment. An economist predicts that the buying power $B(t)$ of a dollar $t$ years from now will be given by $B(t)=(0.95)^{t} .$ Use the graph of $B$ to approximate when the buying power will be half of what it is today. Approximate the function at the value of $x$ to four decimal places. Take the ln of both sides to obtain x-3 = ln y or x = ln y + 3 3. Use the sliders below the graphs to change the values of b, the base of the logarithmic function y = log b x and its corresponding exponential function y = b x. (b) Estimate the zeros of $f$.$$f(x)=\pi^{0.6 x}-1.3^{\left(x^{1.8}\right)} ; \quad[-4,4]$$(Hint: Change $x^{1.8}$ to an equivalent form that is defined for $x<0$. (a) Approximate the percentage of basic words lost every 100 years. Find a simple exponential function of the form $y=a b^{\prime}$ that models the cost of a first-class stamp for $1958-2009,$ and predict its value for 2020 . One hundred elk, each 1 year old, are introduced into a game preserve. ), Graph $f$ on the given interval. Graph, on the same coordinate plane, the line $y=k$ and the Gompertz function with $k=4, a=\frac{1}{8}$ and $b=\frac{1}{4} .$ What is the significance of the constant $k ?$, The logistic function, $$y=\frac{1}{k+a b^{x}} \quad$ with $k>0, a>0,$ and $0.

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