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Mathematics

1 answer:

ankoles [38]3 years ago

6 0

Answer:

5 feet.

Step-by-step explanation:

We have been given that about 15 feet from the center of the carousel. Allison rode a horse about 10 feet from the center of the carousel.

To find the distance covered by Carl's horse more than Allison's horse we will subtract covered by Allison's horse from the distance covered by Carl's horse.

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Suppose f is a function with exponential growth and f(0)=1. Explain why f can be represented by a formula of the form

galben [10]

We are supposed to explain why the given function can be expressed in form $f(x)=b^{x}$ , when $f(0)=1$ .

Since the given function is an exponential function we can express it as $f(x)=a(b)^{x}$ .

Now let us substitute x=0 in the given function,

$f(x)=b^{x}$

$f(0)=b^{0}$

$f(0)=1$

Let us substitute x=0 in our function.

$f(0) = a(b)^{0}$

$f(0) = a\cdot 1$

$f(0)=a$

Upon substituting a=1 in our function we will get,

$f(x) = 1(b)^{x}$

$f(x) =(b)^{x}$

Therefore, our function f can be represented by the formula of the form $f(x)=b^{x}$ .

7 0

3 years ago

Read 2 more answers

How do I solve these problems?

lesya [120]

$Domain:\\D:x > 0\\\\\ln x=5.6+\ln(7.5)\ \ \ \ |-\ln(7.5)\\\\\ln x-\ln7.5=5.6\ \ \ |Use\ \log x-\log y=\log\dfrac{x}{y}\\\\\ln\dfrac{x}{7.5}=5.6\ \ \ \ |use\ \log_ab=c\iff a^c=b\\\\\dfrac{x}{7.5}=e^{5.6}\ \ \ \ |\cdot7.5\\\\\boxed{x=7.5e^{5.6}}\in D$

$\log x=5.6-\log7.5\ \ \ \ |+\log7.5\\\\\log x+\log7.5=5.6\ \ \ \ |use\ \log x+\log y=\log (xy)\\\\\log(7.5x)=5.6\ \ \ \ |use\ \log_ab=c\iff a^c=b\\\\7.5x=10^{5.6}\ \ \ \ |:7.5\\\\\boxed{x=\dfrac{10^{5.6}}{7.5}}\in D$