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A population of 1,500 insects grows exponentially by a factor of 3 every week. Select all equations that represent or approximate the population, \(p\), as a function of time in days, \(t\), since the population was 1,500.
\(p(t) = 1,\!500 \boldcdot 3^t\)
\(p(t) = 1,\!500 \boldcdot 3^{\frac{t}{7}}\)
\(p(t) = 1,\!500 \boldcdot 3^{7t}\)
\(p(t) = 1,\!500 \boldcdot \left(3^\frac17\right)^t\)
The tuition at a public university was \$21,000 in 2008. Between 2008 and 2010, the tuition had increased by 15%. Since then, it has continued to grow exponentially.
Select all statements that describe the growth in tuition cost.
The tuition cost can be defined by the function \(f(y) = 21,\!000 \boldcdot (1.15)^\frac{y}{2}\), where \(y\) represents years since 2008.
The tuition cost increased 7.5% each year.
The tuition cost increased about 7.2% each year.
The tuition cost roughly doubles in 10 years.
The tuition cost can be approximated by the function \(f(d) = 21,\!000 \boldcdot 2^d\), where \(d\) represents decades since 2008.
Here is an exponential graph that represents \(g(x) = a \boldcdot b^x\). Find the values of \(a\) and \(b\). Show your reasoning.
The number of fish in a lake is growing exponentially. The table shows the values, in thousands, after different numbers of years since the population was first measured.
| years | population |
|---|---|
| 0 | 10 |
| 1 | |
| 2 | 40 |
| 3 | |
| 4 | |
| 5 | |
| 6 |
The value of a home increases by 7% each year. Explain why the value of the home doubles approximately once each decade.
Here is the graph of an exponential function \(f\).
The coordinates of \(A\) are \(\left(\frac{1}{4},3\right)\). The coordinates of \(B\) are \(\left(\frac{1}{2},4.5\right)\). If the \(x\)-coordinate of \(C\) is \(\frac{7}{4}\), what is its \(y\)-coordinate? Explain how you know.