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The probability that a couple will have \(n\) baby boys in a row is given by the formula \(\left(\frac{1}{2}\right)^{n}\). Find the probability that a couple will have four baby boys in a row.

If an investment of \(\$ 1,000\) doubles every seven years, find the value of the investment after 28 years.

If \(P\) dollars are invested at a rate \(r\), compounded annually, it will grow to \(A\) dollars in \(t\) years according to the formula $$A=P(1+r)^{t}$$ How much will be in an account at the end of 2 years if \(\$ 12,000\) is invested at \(5 \%,\) compounded annually?

If \(P\) dollars are invested at a rate \(r\), compounded annually, it will grow to \(A\) dollars in \(t\) years according to the formula $$A=P(1+r)^{t}$$ How much will be in an account at the end of 30 years if \(\$ 8,000\) is invested at \(6 \%,\) compounded annually?

If \(P\) dollars are invested at a rate \(r\), compounded annually, it will grow to \(A\) dollars in \(t\) years according to the formula $$A=P(1+r)^{t}$$ Guess the answer to the following question. Then use a calculator to find the correct answer. Were you close? If the value of \(1_{c}\) is to double every day, what will the penny be worth after 31 days?

If \(P\) dollars are invested at a rate \(r\), compounded annually, it will grow to \(A\) dollars in \(t\) years according to the formula $$A=P(1+r)^{t}$$ Describe how you would multiply two exponential expressions with like bases.

If \(P\) dollars are invested at a rate \(r\), compounded annually, it will grow to \(A\) dollars in \(t\) years according to the formula $$A=P(1+r)^{t}$$ Describe how you would divide two exponential expressions with like bases.

If \(P\) dollars are invested at a rate \(r\), compounded annually, it will grow to \(A\) dollars in \(t\) years according to the formula $$A=P(1+r)^{t}$$ Is the operation of raising to a power commutative? That is, is \(a^{b}=b^{a} ?\) Explain.

If \(P\) dollars are invested at a rate \(r\), compounded annually, it will grow to \(A\) dollars in \(t\) years according to the formula $$A=P(1+r)^{t}$$ Is the operation of raising to a power associative? That is, is \(\left(a^{b}\right)^{c}=a^{\left(b^{6}\right)} ?\) Explain.