0. Functions

Exponential Functions

0. Functions

Exponential Functions

Struggling with Calculus?

Join thousands of students who trust us to help them ace their exams!

Multiple Choice

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$)^{x}$

Exponential function, $f$\left$(4$\right$)=410.06$

Exponential function, $f$\left$(4$\right$)=15.19$

Not an exponential function

Verified step by step guidance

Identify the general form of an exponential function, which is f(x) = a * b^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent.

Compare the given function f(x) = 3(1.5)^x with the general form of an exponential function. Here, 'a' is 3 and 'b' is 1.5, confirming it is an exponential function.

To evaluate the function at x = 4, substitute x with 4 in the function: f(4) = 3(1.5)^4.

Calculate the value of (1.5)^4. This involves multiplying 1.5 by itself four times.

Multiply the result from the previous step by 3 to find f(4). This will give you the value of the function at x = 4.

6:13m

Watch next

Master Exponential Functions with a bite sized video explanation from Patrick

Related Videos

Related Practice

Textbook Question

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?

Textbook Question

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.

views

Textbook Question

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?

views

Multiple Choice

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

Graph the given function.

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

277

views

Textbook Question

A culture of bacteria has a population of $150$ cells when it is first observed. The population doubles every $12~$\text{hr}$$ , which means its population is governed by the function $p$\left$(t$\right$)=150$\cdot{2^{\frac{t}{12}$}}$ , where $t$ is the number of hours after the first observation.